Some important software that aren't games, but will be mentioned rather a lot.
WineX is an expansion by TransGaming of the Wine Project. It's intent is to allow Windows games to run on Linux. They maintain lists of the games that work, those that need a little help, and those that don't. If you subscribe to WineX, you can even vote on which games they should strive to make compatible next. Some people don't like WineX as it may actively discourage developers from porting their games to Linux.This is a tad controversial, as it in no way promotes the development of commercial games for Linux, and in fact enables companies to completely ignore our pleas for native games. That being said however, it does let us play some very good games without waiting for a port.
The primary problem with WineX for running games is that it is not Windows, and thus can have some weird quirks. Even in games that work "perfectly" there may be sound glitches, and graphics slowdown. http://www.transgaming.com/
Open Graphics Library. Used for 3D graphics. The Linux library for this is called Mesa, and is installed by most distributions. http://www.mesa3d.org/
Simple-DirectMedia-Layer.
A set of libraries that are designed to allow you to make a game that works under Windows as well as Linux. Has many add on libraries, website: http://www.libsdl.org/index.php