Shuriken can be bought very early in the game as soon as the Merchant shows up. The merchant is usually the second NPC to appear in the player's house. Shuriken are inexpensive, do decent damage, have high attack speed, high range, go through any enemy they hit, hitting large enemies twice or three times in the process, and have a chance to be able to be recovered and used again.
Molotov Cocktails. With a little Sand, Stone, Wood, Gel, Cobwebs, and Iron, you can make these fairly early. They do a lot of damage for the early game, and the only consumable ingredients you need for the molotovs themselves are the wood, gel, sand, and cobwebs. These improvised firebombs make short work of pretty much every monster and even some bosses before you enter Hardmode. The 1.3 Big Update adds Pink Gel to the ingredient list and reduces the raw damage, but molotovs still remain a powerful tool in pre-hardmode Terraria. 1.4.4 further boosted their utility by replacing the Pink Gel in the ingredient list with plain old gel, making them much easier to craft.
The floating islands. You could find the indispensable, fall-damage-removing Lucky Horseshoe, the powerful Starfury, or the jump-improving Shiny Red Balloon, as well as large amounts of Gold/Silver ore, from which you could make better armour out of in the early game. This is partially balanced out now by the existence of the harpy enemies who spawn at that level and attack player as long as they are up that high. 1.2 makes it even more worthwhile to raid Floating Islands, as you can now harvest actual clouds and Skyware deco furniture and bricks in addition to the loot in the chests. Ever since 1.4.1, the Fledgling Wings now appear instead of the Lucky Horseshoe. They allow you to fly for a short period of time and negate fall damage, being the only set of pre-hardmode wings.
The Extractinator makes amassing ore and gems pre-hardmode practically effortless, as the extremely common slush and silt blocks tend to spawn in massive veins that are easy to clear out. Not only does it make getting some of the best armor and weapons early game easy but it also drops coins, up to and including the extremely rare platinum coins, essentially making money a non-issue until hardmode. This is balanced out by the fact that the Extractinator can only be found in underground desert shacks, which can be hard to navigate early on but once you do find one, the early game becomes significantly easier. Once you gain access to Chlorophyte Ore after those Hardmode mechanical bosses, it can be upgraded with expanded functionality.
Christmas Presents and Halloween Goodie Bags can give a serious head start to any player's arsenal, in addition to seasonal random drops. Getting, say, the Red Ryder rifle from a present even before you go Underground for the first time is entirely possible, as is randomly getting the Machete from some mook at a similar time.
Daring players can wade into the Ocean in hopes of finding a Water Chest with a Trident inside. That trident, with all the benefits of the Spear class of melee weapons, will have enough attack power to last you a good while in pre-hardmode Terraria. If you're even more prepared, you can even bring a Recall Potion (that is easily found in Surface wooden chests) and teleport straight out of the sea before you run out of breath and escape mostly unscathed with your loot.
If you're canny enough to survive in the Marble Cave mini-biome, Hoplites drop Javelins, which are strong throwing weapons for the early game and are dropped in large stacks.
If you're lucky enough to find an Enchanted Sword Shrine underground, it has a chance of dropping an Enchanted Sword, a powerful beam-shooting melee weapon that is capable of carrying you through to Hardmode. If you're even luckier, it can also drop the rapid-slashing Arkhalis or Terragrim (depending on version).
Fishing can net you several helpful items as soon as you can get some bait and a rod together. In addition to items you can fish up (such as potion ingredients, explosive Bomb Fish, and a jump-enhancing Balloon Pufferfish), you can also get crates, which can contain further items like the Tsunami in a Bottle, which grants a second jump, or the Falcon Blade, a fast and powerful (if somewhat short) sword you can get well before you can craft anything that surpasses it, and in hardmode, you can get a fair bit of hardmode ores before you even break any of the altars, possibly ending up with the best set of armor and weapons as soon as you start hardmode if you're lucky. Fishing in the Ocean biome may nab you a Reaver Shark, a pickaxe formerly powerful enough to enable severe Sequence Breaking; nowadays it's equivalent to Gold/Platinum, which is still pretty good for how early you can get it.
Eaters of Souls in the Corruption have a small chance of dropping Ancient Shadow Armor, which is functionally identical to the Shadow Armor crafted with drops from the Eye of Cthulhu and Eater of Worlds and outclasses almost any armor you can craft early on. If you're good at dealing with the Eaters and get a bit lucky, you can basically get the entire Shadow Armor set without having to fight a single boss.
The Slimy Saddle, a relatively common (25% in Normal mode, 50% chance in Expert) drop from King Slime. It allows you to ride a friendly blue Slime; while riding the slime, the player is immune to fall damage, can Goomba Stomp enemies, and is a fair bit faster than the usual un-augmented run speed. Furthermore, once you get a Double Jump, you can reach ridiculous heights by using it while riding the mount. Savvy players can use the Slime's bouncing goomba stomp ability to literally ride bosses and tough enemies. If you happen to have obtained a gun, bow or boomerang, you can freely continue to attack them as you do so, allowing you to rack up absurd damage numbers in a very short timespan, or even ride the Eye of Cthulhu into the stratosphere by repeatedly stomping off of it. It renders every pre-hardmode boss but the biome-restricted Queen Bee a joke, and it remains an incredibly helpful mount even into Hard Mode, as long as the player is smart about using it.
The Worm Scarf, a guaranteed drop from the Eater Of Worlds' treasure bag in Expert mode. It gives you a flat 17% damage reduction, no strings attached. This is somewhat offset by the fact that the Eater Of Worlds is definitely tougher than its' Crimson counterpart, and is second only to Skeletron in terms of pre-Hardmode challenge. That being said, the Scarf remains invaluable throughout the entire game, and the Eater is still one of the easier bosses overall. Even players who are focusing on a Crimson world often take the time to make a Corruption world exclusively to get the Scarf.
The Jester's Arrows and the Frostburn Arrows can be produced cheaply from the start of the game, and remain some of the better ranged options available until shortly into Hard Mode. The Jester's Arrow penetrates enemies, does solid damage, and lights up its' path of travel; it can even be used for locating caves and ore veins underground. The Frostburn Arrow is not as useful against basic enemies, but it is very strong against bosses, being able to inflict the Frostburn debuff - essentially a more potent version of the On Fire! debuff. The Jester's Arrow becomes even more invaluable in Expert and Master modes, where getting any weaponry that surpasses them is much easier said than done.
The Boomstick can be obtained from the Underground Jungle as soon as the player is either skilled or strong enough to dig deep and find one. It is hands-down one of the best pre-hardmode weapons you'll be able to get your hands on, eviscerating anything that gets into close range in mere seconds. The challenge is surviving the brutal gauntlet of murder that is the Underground Jungle long enough to find one, as they're fairly rare.
The Gravedigger's Shovel is a non-combat example. It allows you to mine a 3x3 square of blocks at once, but only soft blocks, such as dirt and mud. It can be crafted at a Workbench located in a Graveyard for a scant amount of Iron/Lead and Wood; the biggest obstacle to acquiring it is getting a Graveyard mini-biome going, something the game will be only too happy to help you with. Once you have it, it allows you to absolutely power through any soft terrain; this has a myriad of uses, ranging from bulldozing through the terrain in the Underground Jungle and Mushroom Caves to simply digging down through the surface layers with outrageous speed. It will save the player a LOT of time, especially on Expert and Master mode.
If you're good enough at dodging corruption/crimson mobs, you can sneak down into the respective biomes to smash one of the orbs, which in turn lets meteors start spawning. The meteor set is a great early game armor and its set bonus, the space gun costs no mana, is amazing early game, allowing you to tear through mobs and bosses rather handedly.
If you're lucky enough with dungeon spawns, it's possible to get a Water Bolt fairly early on, above the danger line in the Dungeon where the Guardian would promptly spawn to kill you. The Water Bolt is a great magic weapon that bounces off of walls for a set number of bounces. With a proper arena to abuse this, it can absolutely shred through bosses and is great for crowd control early game. This was nerfed in 1.4 but is still possible in drunk world seeds: since the dungeon entrance spawns below the surface in such worlds, the danger line is moved down to compensate, but not the Water Bolt spawning check.
The Snowball Cannon is easily found in Snow Biome Underground Cabins, or from Boreal Crates. It boasts very good damage, ammo for it can be found easily almost anywhere in the Snow Biome, and it has enough stopping power to halt most enemies in their tracks. Competitive weapons are much harder to obtain, especially in Expert and Master Modes. Most critically, it's one of only a few pre-Hard Mode ranged weapons with auto-fire capability.
The Diamond Staff is made from Platinum and Diamond, two relatively common materials (albeit found relatively deep) in the regular underground, meaning it can possibly be obtained within the first hour of gameplay if you spend some time digging or luck out with the Extractinator. For that, you get a fast-firing, relatively mana-efficient, decently high-damaging staff with piercing and auto-fire to boot, which will likely stave off most normal enemies found in pre-Hardmode and hold its own against most of the bosses. It also holds up surprisingly well even once you've got a few boss kills under your belt, and if desired, you can even feasibly use it up until the end of pre-Hardmode.
The Katana can be acquired before defeating any bosses from the Traveling Merchant by purchasing it for 10 gold. Boasting a whopping 19% critical hit rate, autoswing, a fast-attack rate and decent damage, it can last through most of of pre-Hardmode.
Each of the swords that make up the Night's Edge are a Disc-One Nuke in their own right that are leagues stronger than any of the pre-Hardmode ore swords and can all be obtained before beating a single boss (sort of, see below) if you're good enough at traversing dangerous biomes in the earlygame:
The Light's Bane can hit through walls while the Blood Butcherer deals heavy Damage Over Time, and they can be easily crafted with just the Demonite/Crimtane ore veins found underground.
The Blade of Grass deals poison damage and can be crafted with common drops from the Underground Jungle.
The Volcano sets off miniature explosions every time it hits an enemy: it requires you to fight the Eater of Worlds/Brain of Cthulhu at least once to craft a strong enough pickaxe to mine Hellstone, but you can get away with killing just a few of their parts to drop the necessary materials without actually having to beat them.
The Night's Edge itself becomes one in an aforementioned drunk world, and since it was designed to last well into early Hardmode, it utterly wreaks havoc on all of pre-Hardmode.
Hardmode
Ice Golems and Sand Elementals can be fought as soon as you enter Hardmode and enter a blizzard/sandstorm respectively. They can drop Frost Cores and Forbidden Fragments respectively which, with Adamantite or Titanium Bars, allow you to craft Frost Armor and Forbidden Armor, a great option for melee/ranged or magic/summon users respectively. The Ice Golem can also drop Ice Feathers that can give your wings an early upgrade.
Similarly, Biome Mimics can be faced in Hardmode with only a bit of Soul farming, and can drop some fantastic weapons for how early you get them. The Evil Mimics' dart guns are highly damaging and can equip relatively easy-to-make special ammo to give them a major power boost, while the Hallowed Mimic's infamous Daedalus Stormbow will possibly allow you to net yourself a Mechanical Boss kill the night after if you stock up on upgraded arrows.
The Shotgun, an expensive weapon sold by the Arms Dealer in Hardmode, is an ingredient for the Onyx Blaster, whose other ingredients aren't hard to farm. This can craft a reliable, cheap gun that will eviscerate most basic enemies and handily obliterate bosses, even on Master mode. It can take you most of the way to the Moon Lord all by itself.
