Mod background
Mod or modification is a term generally applied to personal computer games (PC games), especially first-person shooters, role-playing games and real-time strategy games. Mods are made by the general public or a developer, and can be entirely new games in themselves, but mods are not standalone software and require the user to have the original release in order to run. They can include new items, weapons, characters, enemies, models, textures, levels, story lines, music, and game modes. They also usually take place in unique locations. They can be single-player or multiplayer.
 Mod safety
Before installing any mods, please note, that mods are not officially a part of Terraria. You must never try to install a mod into the game or server unless it has been updated to exactly match the version of the client you are running. Even a slight variation could be enough to cause problems, including crashing or corrupting your saves/worlds. Mods are typically updated on an irregular schedule shortly after the game itself is updated (though this depends on how quickly the mod author or maintainer gets to it), so there will always be a period following a new release when no mods are safe to use yet.
Mods that only alter the behavior of existing items, blocks, or mobs are fairly safe; they should typically be able to be installed or uninstalled at will, without corrupting your save (although if you have structures that rely on behavior introduced by a mod, then they won't work without the mod installed). Note that this includes mods that add crafting recipes without adding new items/blocks.
Mods that introduce new items, blocks, or mobs are not safe to uninstall. Once you have saved a new item/block/mob into your world, you must never play that world without having the mod installed, or you risk crashes or corruption (no, not that kind of corruption.) (Should you wish to uninstall the mod, you must either abandon your previous saves that used it, or ensure that you destroy all of the new items/blocks/mobs in your world before removing the mod.)
If you are going to install a mod, however, that adds new blocks, items, etc., you should probably save a backup of your "Terraria" folder in "Program Files/steam/SteamApps/common". One mod that I do suggest(Not really a mod, but helps you install others) is Game Launcher. Game Launcher allows you to have multiple copies of Terraria and be able to downgrade your version(for older mods).
Multiple mods may conflict with each other; certainly if two mods need to alter the same files, then they are unlikely to be compatible.
 Mod list
- Terrafirma - Makes a handy map of your world in a couple of clicks. Shows statues, chests and furniture all with individual, customisable, colour coded icons. It can also search the world for a certain block type and highlights it helpfully.
- Rom Terraria v2.0 - Adds things like a mini-map a clock and weather effects. It also has an "enable infinite blood moon" setting... sounds fun!
- TerrariViewer(Terraria Inventory Editor) - Are you too lazy to actually find all the banner?. Have you started another world and realized you can't be bothered any more? Yes? Then this mods for you! Allows you to give yourself any item you want, simple!
- Terraria Server Browser - From the makers of "Terraria Inventory Editor" comes this handy server finding tool. It shows a list of servers each with name, state, ip address and even a description. Plus, it looks a bit like the TF2 one.
- TNT Cannon - Star cannon not powerful enough for you? How about a gun that shoots dynamite? I would suggest not using it near your NPC village, unless you're that type of person... Also has poison knife, shuriken and glowstick launchers.
- Constant Goblins - If you love goblins this mod's for you! Some goblin-lover decided that the goblin army didn't visit enough so they made this mod, with it they visit every day!
- Obsidian Mod - Obsidian mod is a mod that intends to greatly enhance your terraria expereince. It adds a lot of new cool, original and USEFULL items and a whole parallel universe. If you think the 1.2 update didn't add enough get this mod!
- TerraMap (Terraria World Map Viewer) - An interactive Terraria world map viewer that loads quickly and lets you pan and zoom, find and highlight blocks, ores, items in chests, dungeons, NPCs, etc. It also supports headless, unattended world map image generation via command-line, complete with highlight capability. Compatible with Terraria 188.8.131.52.