Fire Emblem's AI uses a method of determining target priority that leads to what many human players might consider very odd decisions. Enemies often target units that they can't actually damage, or they may attack less relevant units when they could much more easily target your Lord or other, more significant units. This is mainly due to the fact that the AI generally tends to prioritize causing fatalities above all else, meaning they attack all things in range and especially target units with HP below a certain threshold (ignoring the probability of actually hitting or causing damage to any given unit) or if they have a crit chance (even if that chance is in the low single digits). This system was implemented from the fifth game in the franchise onward in order to keep the game moving along at a decent pace; earlier games would have units ignore characters with very high Defense or Evasion stats, which made for some long, tedious battles.
The AI is programmed to avoid counterattacks if possible—if it can attack a unit without receiving a counter, it will almost always do so, unless it can kill something. This means that, for instance, the AI may ignore a Squishy Wizard in favor of chucking handaxes at a sword-wielding paladin on a fort, even if one would die in two hits and the other can tank a dozen.
The vast majority of bosses in maps with a Seize objective, and very often ones with a Kill Boss or Rout objective, will not move. For Seize bosses, this makes some sense — if they move off the objective, then they effectively forfeit the chapter, and being on a throne or gate provides some pretty hefty defensive bonuses — but Kill Boss and Rout bosses really have no reason to not face the player alongside the rest of their troops. It's especially silly if the boss doesn't have any ranged weapons, in which case the player can simply plink them to death with bows, magic, handaxes, and javelins, while the boss just sits there and wonders where their life went wrong.
Neutral units fall into this, especially if they're the ones you have to talk to and recruit. For instance, when Erk shows up in the second story arc of The Blazing Blade, he comes out of a village and polishes off two mounted units before you get to him. If you don't get to him immediately thereafter, though, he'll run off and provoke a boss with high Resistance and physical attack.
They also have a tendency to attack enemies that you don't want attacked just yet (usually because they have an item that can be stolen), throw themselves at enemies far more powerful than they are, and always make their moves in the exact same order, which means that on the rare occasions that one of them does have some sense of self-preservation, they'll often retreat when it's really not necessary. And they always retreat when it's time to heal, even if they're using a healing item. Even if it means leaving a plot-sensitive character exposed.
An infamous one is Thea's Pegasus Knights in chapter 11A of Binding Blade. The archers in the same map are fairly easy to corral and will happily walk to their retreat point, but the Pegasus Knights prioritize trying to get some licks in over retreating, and they're so mobile that they count about a quarter of the map as their strike zone. This will usually result in them (including Thea, if Shanna didn't talk to her) hurling themselves one by one into either the boss or the cavalry reinforcements. Pretty much the only way to get them to survive is to kill the boss before they've even shown up.
The AI also has a tendency to ignore your equipment, meaning that flying units will attack Mages with wind magic and armored units will attack Swordmasters (who, like Mages, have low defense and high avoid) with Armorslayers.
Then you get the units who are so outclassed by every player unit in range that it's literally impossible for them to actually do any damage (because they have zero chances to hit or no expected damage — or both) but insist on attacking anyway.
Enemies also have absolutely no experience with such advanced concepts as "strategic retreat", "regrouping", or "mixed unit tactics" beyond, as stated above, going after the most vulnerable unit available. However, this is circumvented by good level design and the player's general mindset… Usually. Having a single little soldier charge blindly at you when his allies are still too far away to assist is an unfortunately common occurrence.
There's the behavior fans have termed "Matthis Syndrome", which involves recruitable enemies attacking the very characters who can recruit them. This often leads to absolutely ridiculous cases of Gameplay and Story Segregation, most notably with the character it's named after, who will willingly attack (and most likely kill) his sister Lena, all the while calling out for her in his battle quote. He's the most famous example, but there are others, such as Astram having no qualms about attacking his lover Midia or Wendell openly attacking you despite saying he has "no love for war". Granted, some enemies in the series are smart enough not to attack their friends/relatives/lovers, but it's impossible to know which without risking it.
Another good example of this is Thea from Fire Emblem: The Binding Blade… again. She (and her unit of Pegasus Knights) can attack her sister Shanna or her boss Klein (whom she even has a conversation with at the start of the map). And since Klein is a Sniper, if he gets attacked at range, he'll pretty much kill them in one shot. Klein himself can also potentially kill his little sister Clarine in the same level.
This reaches critical mass in Fire Emblem: Awakening, where Cynthia and potentially Yarne can fight and kill/get killed by their own future parents. Justified in Sumia, Panne, and their husbands' cases, since they're unaware of who they're fighting, but still…
And sometimes units who can recruit themselves by talking to a certain character will prioritize doing so over staying alive. Palla and Catria are a good example: the first thing they do after spawning as reinforcements is fly over to Marth and talk to him. The problem is that the map where this happens is full of archers, and Palla and Catria are the first units to move on the enemy phase. This means that, if Marth is standing in range of an archer, they will fly to Marth, recruit themselves, and then immediately get shot and killed, before the player even has the chance to control them.
The cardinal rules for Fire Emblem AI are simple: 1. Absent being scripted to stay put, a unit will attack if an enemy is in range, even if it will both inflict zero damage and die on the counter. 2. The AI hatesyou, the player, specifically, and will prioritize attempting to kill your characters over actually completing its theoretical objectives.
And then the Conquest route of Fates averts rule number 2: if the enemy's goal is to cross a line on the map (such as the infamous Chapter 10), the AI knows this, and it seems to have at least one turn of lookahead — if it's a choice between attacking Corrin or moving out of range so it can reach the objective next turn, it will ignore 12 games of precedent and ignore combat odds with Corrin for the chance of winning the map outright.
It also subverts rule 1: if it inflicts zero damage on an attack, it will not attack that specific target, even if they're the only one around. They will still actively commit suicide on someone they can harm, however.
In some games, if the AI uses status staves while multiple units are in range, it will always target the unit lowest in the deployment order. In some games, this can be worth keeping a manakete around, even if they don't fight, because as long as you put them last in deployment and with the bulk of the army, it's extremely likely that the AI will go after their massively overkill 20+ Resistance and not your wyvern rider with 4 Resistance or your bishop capable of healing it instantly. Add the fact that these staves tend to wear out after only a handful of uses, and parking a manakete in status range for a few turns becomes a funny way to just flat-out solve the problem.
In the GBA games, the AI is programmed to only use Silence if it detects a character with a Magic stat and a staff in their inventory. This is meant to make it so that the AI will prioritize silencing characters who could otherwise heal the condition, but it also means that an otherwise powerful mage or sage can be rendered completely untargetable by simply having them not hold staves during the enemy's turn.
The AI in Genealogy is notorious for vacillating between "actually pretty smart, if probably not sufficient to battle the player's powerhouses" and "can't chew its own food without assistance." Reportedly, the degree of intelligence is linked to whoever's commanding the troops, with leadership stars marking particularly smart commanders, but it's still not uncommon to see mages or javelin-wielders charging into melee.
The Quirky Miniboss Squad of Falcoknights in the final chapter have the ability to use the Triangle Attack, which, if they pull it off, will pretty much always kill the opponent. But because the Triangle Attack requires them to all group up next to an opponent, and their AI is programmed to move away after attacking, they will pretty much never get into a position where they can use it.
Chapter 2 has you dealing with Princess Lachesis's three mediocre Paladin bodyguards who are very suicidal when there are enemies in their ranges. These knights will surround their princess by default, so if you want to play defensively or don't want to risk having them killed off in order to obtain the very valuable Knight Ring you're given if the three and their Princess survive, you have to keep Lachesis miles away from the incoming enemies, which sucks because she's a prime example of Magikarp Power.
Arvis, when fought in Chapter 10, has two weapons: the Valflame tome, and a silver blade. It's rather understandable that he will pretty much exclusively use the former, since it's much, much stronger. However, if you get him silenced, he will still stick with Valflame, even though he can't attack with it. This does make some tactical sense (Valflame gives large defensive statboosts, so trying to outtank the player until Silence wears off would make sense), but he won't even attack you on enemy phase with the silver blade.
The AI does not notice the Miracle skill, which vastly increases a unit's Avoid if they're on low health. (To be fair, the player doesn't see the Avoid boost either, but you'd think the AI would take it into account.) This means that even though a unit with Miracle and 1 HP is effectively unhittable, the AI will hurl all its units in range into hunting them down, under the impression that their accuracy is the same as always and it's about to kill a unit.
The AI, like the player, can use the Capture command, and will do so whenever it thinks it can get away with it — this is a good plan, since a captured unit is treated as dead until freed, and even if the AI doesn't keep the unit, it can steal all the character's items in the meantime. The thing is, it also cuts the stats of the capturer considerably. Because of this, many players exploit this by deliberately moving an unarmed unit to the frontlines so that the enemy will try to capture them, since the AI prioritizes capturing over being able to actually secure the capture. This means a normally formidable enemy wastes their turn and cripples themselves in the process, allowing you to easily kill them and free your unit.
The AI in Path of Radiance seems to prioritize doing damage/lowering their own damage taken above actually killing your characters — for example, putting Nasir in range of Ashnard will cause him to attack Nasir even if he could kill Ike with his next hit.
Ashnard will also attack Nasir at melee range, even though his weapon can attack at range (and Nasir then can't counterattack).
In Part 1 Chapter 9, you are forced into using only two units: the Squishy Wizard Micaiah and the Black Knight. Since the enemies are there specifically to kill Micaiah and the Black Knight is there specifically to protect her, you'd think they'd send the entirety of their oddly large force at her at once. Nope, they go two or three at a time and hack at the first living thing they see.
Even more fun is that enemies will always, always go straight for an unarmed unit, as they (obviously) can't counterattack (or if laguz or staff-users, not very well). You can easily get Micaiah to level 20 without a problem on that map by parking the Black Knight somewhere with his sword unequipped and letting the enemies flail pointlessly at him while Micaiah whittles them down from afar.
Radiant Dawn emphasizes "no counterattacks!" above all else. Archers will shoot your heavily armored (but melee-only) knight while ignoring the squishy priest holding a weak light magic tome.
Which extends to neutral/allied units as well. Particularly noticeable in 3-10, where, for example, the leader of the Crimean Knights, Geoffrey, will move right up to a Bishop and then not attack them, but then Astrid will take a shot with her longbow. (Thankfully, the longbow is very inaccurate, as this was one of those situations described below where the enemy was being spared for thieving purposes.)
Part 3's Prologue has a rare example of this used for Gameplay and Story Integration. The map's objective requires Skrimir, your NPC ally, to reach the Arrive point. Making things complicated is that his AI will prioritize killing enemies over completing the objective if there's any around the destination, forcing you to clean up the area to end things in a timely manner. As Skrimir is a Blood Knight with little grasp of strategy, this is completely in-character.
The Radiant Dawn AI also prioritizes units who have "rescued" someone. In theory, this makes sense, since if you rescue someone, the rescuer loses half Skill and Speed, making them sitting ducks who can't hit the broad side of a barn. Except tanky units don't care (at least for survival), and more importantly, they still do that if the rescuer has the skill that nullifies the stat penalties, meaning Tibarn (who starts strong and has that skill) can easily make all enemies flock to him and kill them on counterattacks, just by grabbing someone. Who needs Provoke?
In Awakening, NPC characters are even brain-deader than usual for the series. Paralogue 3, involving the players escorting a group of villagers, will have said villagers running straight into the enemy's waiting swords when they would be safe if they just stayed put or tried to keep out of the attack range. The villagers in this mission are actually following a fixed route towards the bottom corner of the map (the prior cutscene establishes they're fleeing in a blind panic) and will escape if they get there, but since that's going right through a thicket of enemies and the mission is usually over before they get close, it makes them seem like lemmings.
The AI also pays no attention to a player unit's pair-up partner. They will gladly rush towards that unarmed Troubadour, completely oblivious to the fact she'll be replaced by a General by the time they get there.
There's a paralogue where you recruit Severa. Her paralogue has a trick: she won't automatically join your group when either Chrom or Severa's future mother Cordelia are sent to talk to her, but you have to escort her to another spot in the map so she can talk to an NPC Villager she had befriended. (You better not kill that Villager, doing so requires facing Severa's wrath to the point of a Face–Heel Turn!) Her poor AI causes more trouble in such a mission, as she tends to attack nearby enemy units to the point of dying... or sticking to the northern wall where the Tricksters can nearly one-shot her with their Levin Swords.
The AI in Fates generally understands the pair-up mechanics pretty well, barring the fact it will never dynamically create or split support pairs (let's face it, the game would be even more unreasonably Nintendo Hard if it did). It will even switch a paired unit around to get an advantage. However, it shows no foresight in doing so, and will only switch for immediate benefit, and not to allow the flying back partner to completely flank the player.
Similar to the Awakening paralogue, Fates includes a bunch of actively suicidal villagers in Sophie's paralogue. This time, they start in a perfectly safe corner and will actively run towards the nearest enemy.
Shadows of Valentia has an AI that will pull units back to heal if their health gets low, which makes sense on its own. Then you realize that only the people near death retreat to healing spots, and they do it without attacking anyone in their way (even if they have no fear of counterattack). Finally, the AI sends everyone near death, often not accounting for the limited healing spaces if they don't have healers, meaning they send near death people to heal, then leave that one behind while the rest start to head back to fight. This makes it stupidly easy to cut the enemy army in half, even if it's mostly temporary. A good way to take advantage of this is to have an archer or two sit in the path between the enemy army and a healing spot and let loose. (Keep in mind that this doesn't affect summoned units, which the AI just summons more of anyway.)
Witches are able to teleport anywhere. Instead of being the bane of players like one would expect, they're a prime example of A.I. Roulette. Most of the time they'll go for Archers or Mages, who are able to fight back at them, instead of someone who can't. However, they do have a tendency to at least go to a space where they can get an Avoid bonus… which doesn't mean anything if they're against a magic-user, since magic negates field bonuses in this game.
Delthea is a great example of this. She, a mind-controlled enemy, must survive the chapter in order to be recruited, but it's very hard to predict what she'll do with her Teleportation skill. Sometimes she'll wait until you get close enough to the boss to attack, sometimes she'll teleport on her very first turn and attack, and she'll even attack her own brother, Luthier (making her a case of the aforementioned "Matthis Syndrome"), who can counterattack and possibly kill her.
Outside battle, the Garreg Mach NPCs don't have particularly good pathfinding skills. This can result in impasses between NPCs who were in each other's path or scenarios like this.
Rhea: Yes, let us work together. It reassures me to have you by my side. BigKlingy: "After all, as you can clearly see here, the man currently by my side is an idiot."
In Chapter 1, your foes are inexperienced students in a mock battle in which they aren't fighting to the death. Naturally, they make extremely bad tactical decisions, such as putting an unarmored archer on the front lines or going Leeroy Jenkins out of formation.
Annette's paralogue features several enemies that will only attack her no matter what. Should she be unreachable, they'll minimize distance towards her, but otherwise wouldn't even try to kill your units who block access to Annette. All of these units have range 1, which makes them perfect target practice for anyone with magic or a bow.
In chapter 14 of any Non-CF route, the defense of Garreg Mach can result in some. For one, the enemies here exhibit Artificial Brilliance in knowing that reaching one of the defend points will give the player a Game Over and actively try to do so. Thus, the enemy prioritizes reaching a defend point above all else. However, once it has reached said tile, it still cannot resist the urge to attack anything in range. Thus, once an enemy has moved onto a defend point, it can still attack one of your units, and potentially die on counterattack, when not attacking at all would have been a Game Over for the player.
Hubert's Paralogue, which involves protecting several mages from Demonic Beasts, zig-zags this. The mages start out using Gambits, which destroy the Demonic Beasts' barriers and don't allow the enemy to retaliate, which is a smart choice for the situation. Unfortunately, when those Gambits run out, the Mages fight back against the Demonic Beasts with their spells in close quarters, which will allow the Demonic Beasts to retaliate and likely kill them. Lord Arundel then insults you for being unable to protect them.
While most of the examples of stupidity in Heroes are typical to the series, the skill system means that a new case is added: assist skill loops. Units who aren't in range of enemies will prioritize using assist skills over anything else, meaning that it's possible for the AI to get caught in loops of doing nothing but using assist skills on each other while ignoring the player's units. For example, a unit might use Pivot to jump over their ally each turn, only for that ally to use Reposition to bring them back to their starting square, and then keep doing this until the player brings their units into range.
Another assist-related example comes from enemy units Assisting their allies into places where they can't move, such as an infantry unit repositioning a cavalry unit into a square surrounded by forest and ocean tiles. In particularly bad cases, units might be assisted into places where the player can't reach without appropriate units, either, creating an soft-lock that can only be resolved by surrendering.
Leif's Engage Skill allows his users to always counter enemy attacks with the most advantageous weapon, even if it wasn't currently equipped, which sounds amazing - a foolproof way to avoid being Broken and to counterattack at any range! However, when it comes to deciding which weapon is most advantageous, the AI can be a bit... single-minded. In particular, it really likes to equip the Light Brand, a magic sword which is very good on units with high or even decent Magic stats, and very bad on units without them. Naturally, low magic units are just as likely to end up with the Light Brand foisted unceremoniously upon them.
While enemies with status staves usually display Artificial Brilliance, Fracture users are the exception. They'll always use their staves if someone is in range, even if no other enemies can attack that unit (and therefore inflicting Break is entirely pointless). They don't have especially good target priority even if enemies are in range of a unit.
Smash weapons force the user to strike last when initiating combat. Enemies with Smash weapons will often throw themselves at members of your army who'll kill them in two hits, getting themselves killed before they have a chance to strike.
In the DLC, Enemy Mage Cannoneers will frequently use their Let Fly ability (a long-range Area of Effect shot) on empty ground, in places where your units can't even reach.
, he will still stick with Valflame, even though he can't attack with it. This does make some tactical sense (Valflame gives large defensive statboosts, so trying to outtank the player until Silence wears off would make sense), but he won't even attack you on enemy phase with the silver blade.