Mods

Mod Safety
Mods are currently not officially supported by Mojang, as such users who install and use mods are entirely doing so at their own risk. However, official modding support is in planning. Mods work by editing or adding to the obfuscated source code. This means that mods only work with the Minecraft version they are compiled for.

For example, a mod that edits a .class file of version 1.5 will not be compatible with either 1.4 or 1.6. A notable exception to this is 1.6.5 and 1.6.6, where mods for either one are co-compatible. Also, any mods made in 1.7, 1.7_01, 1.7.2, or 1.7.3 are forwards compatible.

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 making a world save corrupted. Note that this includes mods that add crafting recipes without adding new items or blocks.

Mods that add content, such as blocks, items or mobs, are riskier to uninstall. Since 1.4, modded content is automatically removed from the world if the mods that added them are not installed, thus preventing crashes. This can still cause issues and uncertain behavior, even such as crashing.

Mods that change how chunks are saved will render saved worlds incompatible with 3rd party software not designed to work with them. An example of such tools are map rendering tools, such as Cartograph G, that rely on parsing save files to produce their end results.

Multiple mods may conflict with each other; certainly if two mods need to alter the same files, then they are unlikely to be compatible.

Client Mods
Client Mods are modifications to your Minecraft program (Alpha or Beta). They are not custom clients, and require modification of minecraft.jar. Like high resolution textures, they only work with the launchers, and won't work if you play Beta through a browser.

The most common form of client mods are aesthetic and/or functional. However, some client mods add content to the game, and others fix issues with the game. While some do work on SMP, mods that add content, and thus  could be used for griefing, do not work, as the server will ignore  custom content.

New Content
Any mods that add new blocks or items will have new Data Values, which can be found on the Mods/Data values page.

Introduction
You have to delete the META-INF folder inside the file "minecraft.jar" and replace the files "en_US.lang" and "stats_US.lang" inside the folder "lang" in order to use a language pack.

You can find a complete installation guide for different operating systems on the Minecraft Forums.

Server Mods
Server Mods are modifications to the official Minecraft server software. They generally fall into two broad categories: management and gameplay.

Management mods are commonly designed to make administration of servers easier by implementing tiered privileges for commands (such as kicking, banning etc.). They are frequently implemented as "wrappers" which do not actually modify the main server .jar file, instead monitoring its output and sending commands to it.

Gameplay mods are modifications to actual game mechanics, such as restricting the placement of blocks commonly abused by Griefers (e.g. lava, TNT), fixing bugs in the server (e.g. making furnaces function before the update of 10th of September 2010) or adding new gameplay features.

Mod List
This is a list of wrappers and modifications.

Beta Server Wrappers
There is a full list of server wrappers at the Server Wrapper page