Modifications (or Mods for short) are add-ons that you can download that will change Minecraft's game content adding new experiences and to the game. Most mods in Minecraft add content to the game to introduce new gameplay elements, change how the game looks and feels or add more options in how the player can interact with the Minecraft world.
Generally, the creator of a mod updates the mod whenever the game updates - adding more content, bug fixes, or optimizations - and users will download the latest version of the mod to suit their game version.
Minecraft mods are generally safe to download and install, but one should exercise caution with mods to prevent crashes, deletion of game or save data, system instability, or potential malware infections from a bad link or the mod itself. A useful way to protect your game from such problems, is to back up various files, such as the .minecraft folder, if you choose to use mods.
Below you can find a list of popular mods that you can download for Minecraft versions 1.7.5, 1.7.4, 1.7.2, 1.6.4 and 1.5.2: