What is MUGEN?
This: Video link since Youtube embedding is apparently not supported...
It's a 2D fighting game engine. More importantly, it's the ability to have almost any character you can imagine fight almost any other character you can imagine on any stage you can imagine.
Marvel vs Capcom, Mortal Kombat, Street Fighter, Tekken, Darksiders, you name it, if it's a classic fighting game, there are characters written for MUGEN. Not to mention any number of new or orginial charecters. Green Lantern, Batman, Homer Simpson, Spongebob, Bugs Bunny, Spider-man, Doctor Doom, Deadpool, Wonder Woman, Sub-Zero, Scorpion, Mr. Incredible, you name it, chances are, there is a character for MUGEN. Not to mention a large number of anime characters. In total? I'd number it in the thousands.
In addition, pretty much any background from any fighting game in the last two decades is also probably available for download. Not to mention any number of new and original stages in both lowres (retro) and highres.
There are also any number of early development, WIP, beta, and finished fighting games "remakes" and full original games based on the system. A few worth noting include Shades of Manhattan, X-Men: Second Coming, and Super Marvel is Capcom: Eternity of Heroes to name a few. I also believe there may be an X-Box port floating around somewhere...
Oh, and there are rumored to be torrents preconfigured with a wide variety of characters out there and available for download if you're too lazy to edit some text files, shuffle around some folders, and make your own.
Where can I download?
This is the main page for MUGEN 1.0.
As for characters and stages, where to get them, how to "install them", I'll leave that to you guys. I think you all know our good friend Google. Plenty of tutorials, download links, and communities out there. Chances are you can figure it out.