There are different kinds of mods; many can be used with only a standard copy of Terraria; some are run independent of the game; others can only be used with a special launcher.
These mods expand the game's items, non-playable characters, or features in one way or another. These mods may or may not require the use of another Mod. Read about each mod for instructions on installation. Always remember to backup files that are called to be overwriten.
Buildaria is distinguished from other map editors by the ability to build in-game, instead of through a program. Among other features, it allows copy and paste, unlimited material use, and a "noclip".
Tarra Mod is a multi functional mod to Terraria adding RPG like stats and permanent Skills to player characters, world generator and building, cheats list, new storage option, and special key binding. This Mod is designed to auto update.
Terraria Leveled is a dedicated RPG mod. It adds no items to the vanilla game, but instead focuses entirely on character level up through fighting mobs and mining. Mobs and traps have been modified.
N Terraria is an RPG mod that is great for RPG lovers. You can be of new races other than humans, craft new items, slay new mobs, and battle waves of monsters in the new graveyard biome. This mod allows you to play as a Bunny or a Slime.
Rydian's Terraria Trainer
Rydian's Terraria Trainer is an indirect mod that runs at the same time as Terraria but in a different instance. With this Mod you can: Become invincible and get infinite item use/placement; obtain huge building range to make creating structures easier; fast-forward time to night; obtain infinite wings or rocket boot fuel; have infinite breath; and many more possibilities.
Those these are not actually "Mods", they allow easy access and manipulation of other Mods.
Terraria Custom Content Loader
Terraria Custom Content Loader (TCCL) allows players to add lots of texture, music, and minor functionality changes to Terraria. Includes a handy GUI and helps keep content mods from overlapping.
Detox is a client modification for Terraria that extends the base of what the game can do and adds a layer of customization to the client via the use of plugins. Detox does not modify the client executable that is on disk and does not rely on a specific version of the Terraria.exe, this means that Detox is almost guaranteed to work for any version of Terraria.
tAPI is a program that allows its user(s) to add their own content through the use of Hooking and JSON to Terraria 1.2 and later. This mod is still under development. It will require a legitimate copy of Terraria (purchased through Steam) to be able to be installed.
TOnline Thread: tAPI
Server mods allow special functions with terraria multiplayer servers.
TShock is a server modification which allows you to summon different mobs, items, change the game time and lets you teleport to other players in the server. It also lets you spawn unlimited bosses and buff yourself or others.
External tools are mods that function separately from the game. They are installed and opened without need of the terraria exe and have their own interface.
Terrasavr is a web-based (no downloading needed) inventory editor to mod a characters current profile including colors, equipment, inventory and so on.
TerraFirma is a mapping tool used to view the Terraria world, it allows you to see where all ores and chests are located, as-well as the contents of chests, you can also zoom in and out.
TEdit is a modification as well as a mapping program that enables the user to create chests, blocks, walls and practically anything that comes to your mind. It also is popular because of its ability to create worlds without even starting Terraria (similar to World Viewer). Similar to TerraFirma, you can zoom in/out, see where ore and chests are located. Unlike Terrafirma you can modify how much ore you'll find and can add new treasure to those chests.
Dean's Custom World Generator
Dean's Custom World Generator will allow a user to slightly alter the world generator's algorithms to make a still randomized world with or without the features the user desires. This tool is still in development.
Terraria Save Game Editor
Terraria Save Game Editor (TSGE) is a program to mod Terraria characters. Characters can have all their stats changed (i.e. changed from medium core to soft core), manage and edit the inventory, and edits the character buffs/debuffs.
These mods alter user interface.
XBox Remote on PC
The xbox remote mod helps players with navigating the menus of the console version on XBox.
These mods change the textures of the game or UI without any game play changes. For more textures, please visit the tOnline Forums
The Terraria-Interface-Mod by Testing_1_2 sharpens up the inventory and font in terraria to make a very easy to see UI.
Svard's Fonts and Cursor
Svard's Fonts and Cursor will allow the player to choose from an assortment of fonts and cursors to fit his or her liking.
hq2x is a total texture change; though not very heavy.
Solstice's HD texture pack
Solstice's HD texture pack provides a more granular, high contrast texture for the entire game. (Pre-1.2, but the author is working on it.)