Mugen is a free 2D fighting game engine. It allows you to create your own fighting game (with your own characters, backgrounds...). Mugen is very configurable and powerfull, you can get a gameplay as good as commercial fighting games such as Street Fighter Alpha or King of Fighters series. The only weak point of Mugen is the difficulty to create characters. But the more difficult is to begin, after some work it becomes easier, and you'll love it :). But if you don't have time or patience to make your own characters, you needn't worry: you can download characters already made by other people.

You can download Mugen at Elecbyte's site: http://www.elecbyte.com
If you want to make characters, backgrounds ... you also need to download all things in the Developper section and read Mugen docs.

Note: The current version is for Linux only. If you want to run Mugen on Windows, you need to download an older version of Mugen (just use a search engine to find one).
Note 2: There is a new version of mugen for Windows called WinMugen, but it's not official. So I don't recommand using it.

You can find many links for the latest characters in this site: http://rotb.mgbr.net/mugentopia/

If you want some of the best characters and backgrounds, here is a good site: Neogouki's site