M.U.G.E.N (also known simply as MUGEN) is a freeware 2D fighting game engine designed by Elecbyte, written in C which originally used the Allegro library. The latest versions of the engine now uses the SDL library.
In mugen, you can choose your own characters and stages! From Michael Jackson to Ryu, From Final Destination to London: In Mugen, YOU control the game!
You can also get ScreenPacks that change the look of your mugen: They change the intro, the title screen, the VS screen, the lifebars and sometimes even add their own music!
Here are some screens:


You can also make your own characters and stages by using tools such as Fighter Factory!
Links:
http://www.elecbyte.com/mugen <- Website
http://www.mugen-infantry.net/ <- Mugen Infantry, a great source of characters, stages, screenpacks, lifebars etc.
http://www.mugenguild.com/ <- Mugen Fighters Guild, another great source of resources.