The series in general, or to multiple games at the same time
Alerting enemies to your presence and triggering the Threat Meter will start a short piece of music that is based on the bass-line for early Final Fantasy battle themes.
Occasionally, Prompto will sing the Final Fantasy victory fanfare. While it is a time honored tradition, the only character before this who had ever actually sang the theme upon victory was Kefka in Dissidia Final Fantasy. Big Bad Ardyn himself sings it at the end of Episode Prompto.
The recurring Masamune weapon can be obtained as pre-order/Day One DLC.
Noctis and company will often fight robotic soldiers, dubbed Magitek Troopers. This mix of human soldiers fighting alongside cybernetic lookalikes is reminiscent of Final Fantasy VIII's Estharian army, which also had gun-axe wielding cyborgs battling the heroes. Later in the game, the process for creating Magitek Troopers are detailed, which also connects them with Sephiroth clones.
Gilgamesh is fought during the Episode Gladiolus DLC.
Omega wanders the Insomnia ruins in the Royal Edition as a Superboss.
One of Ifrit's Techniques in Episode Ardyn is named Meteor Strike, which calls to mind the recurring ability/Limit Break.
The game's How We Got Here at the beginning to Ifrit's fight is also a nod to the fact that in some shape or fashion, Ifrit tends to be the first major summon shown in several of the games.
A number of the signs in Insomnia are references to previous Final Fantasy games, as outlined in this Reddit thread.
The aesthetic of the Solheim ruins resembles that of the Crystal temples.
In the tutorial for warping, Carbuncle says "It's warping time!", a reference to one of Gilgamesh's quotes...which is in turn a Shout-Out to Mighty Morphin' Power Rangers.
The mammoth-like Garula enemies in FFXV were originally from this game.
In Comrades, one of Monica's possible quotes after cooking a meal for the crew is "One can't wage war on an empty stomach", which was said almost verbatim by Sabin after eating the food prepared in the dining car of the Phantom Train.
The Niflheim Empire owes a lot to VI's Gestahlian Empire: both command a relatively high level of technology boosted by magic and are led by an old man being manipulated by a deceptively clownish advisor.
Most of the "Machinery"-type weapons that Prompto and Noctis can use are direct references to Edgar's Tools; the Auto Crossbow, Bioblaster, Circular Saw, Drillbreaker, and Noiseblaster.
In Altissia, Noct can encounter a haunted painting of a woman named Lakshmi. The name of the daemon haunting it? Chadarnook, of course.
When Noctis meets First Secretary Camilla in her home, there is a diplomatic meeting where the player can choose various dialogue options and is rewarded with an item determined by how well they did, very similar to a brief mini-game in VI where the party conducts diplomacy with Emperor Gestahl.
The party can encounter Bismarck while exploring with the Royal Vessel.
The first mission of Chapter 14 is titled "World of Ruin." Accordingly, the finale of XV takes a lot of cues from VI, particularly Noctis waking up after a Time Skip to find out the world has gone to hell in his absence and his friends have gone their separate ways, and he rallies them together for a final assault on Ardyn's fortress, a massive skyscraper.
An optional boss in Comrades is Deathgaze, who appears identical to its appearance in VI, complete with a rendition of The Decisive Battle playing during the fight. It also appears in Lunafreya's chapter of Dawn of the Future.
During Aranea's chapter in Dawn of the Future, when she faces Ardyn the novel describes him as "dancing mad".
The final chapter of The Dawn of the Futuretakes even more cues from VI, with Bahamut uprooting the Citadel and lifting it into the sky, just like how Emperor Gestahl and Kefka created the Floating Continent. The finale even involves magic and summons disappearing from the world forever as a result of the death of a tyrannical deity (Bahamut/Kefka).
"Great Glacier Cola" will appear in some gas station refrigerators.
A bar in Lestallum is named "Adamantoise Paradise", a nod to the Turtle's Paradise sidequest.
The Midgar Zolom (here correctly rendered as Midgardsormr) is featured as a rare enemy.
The title of the Moogle Chocobo Festival DLC's mission is "Interrupted by Fireworks", after a BGM track from Final Fantasy VII.
Luna's death mirrors that of Aerith's: both are fatally stabbed by the Big Bad while in the midst of performing a holy ritual. Their poses as they fade away/sink into the lake are also near-identical.
The name "Lunafreya" is reminiscent of Freya Crescent. In addition, the trident being Luna's weapon is one to Freya's Dragon skill "Luna", which is learnt by equipping the trident.
A pair of Zidane's signature Mage Mashers is available as pre-order/Day One DLC.
Sania's series of frog-collecting sidequests is reminiscent of IX's frog-catching minigame/side-quest.
The Lucii appear to be this game's equivalent of the l'Cie, with traits of the fal'Cie: besides the name's similarity to "l'Cie", the Lucii were charged with a divine task by their gods... but much like the fal'Cie, they themselves are rather aloof empowering entities.
The daemons are the equivalent of the Cie'th. They are former humans, altered by a supernatural force related to the power source of the Lucii/"l'Cie". The Japanese term for Cie'th is "Shi-gai" and the Japanese term for daemon is "shigai".
In Platinum Demo, a l'Cie brand can be seen on a playing card in the second area.
Lightning's Blazefire Saber is available as pre-order/Day One DLC.
XIV's version of the recurring Gae Bolg weapon is available as pre-order/Day One DLC.
"Adventurer from Another World" is stuffed to the gills with references to FFXIV. To wit:
When the quest is activated, the "Quest Accepted" audio tune plays while "Accepted" appears on-screen. Similarly, "Complete" appears on screen as the "Quest Complete" theme plays when Garuda is defeated.
The final confirmation prompt for beginning the main portion of the quest resembles the prompt to commence a dungeon or boss fight with FFXIV's Duty Finder.
Y'jhimei's steed is a Fat Chocobo, which FFXIV players can earn with the Collector's Edition.
Some actions when interacting with quest-relevant objects produces a small "Interaction" gauge, similar to in FFXIV.
Y'jhimei's animations in some cutscenes are the same as some emotes for female miqo'te players.
The reward for clearing the quest are "Glamour Prism" items that allow the heroes to turn into different races from FFXIV: miqo'te for Noct, roegadyn for Gladio, elezen for Ignis, and hyur for Prompto. Players can also challenge a stronger version of Garuda to earn Allagan Tomestones to exchange with Y'jhimei for Garuda weapons.
Reddit thread.