I don't think it qualifies as an actual language, but it is so interesting it does deserve a wiki page. Learn more about it here:

http://www.muppetlabs.com/~breadbox/bf/

and

http://cydathria.com/bf/brainfuck.html

not to mention

http://www.hevanet.com/cristofd/brainfuck/brainfuck.html

Also lo and behold the classic "[99 Bottles of Beer]" written in brainfuck:

http://99-bottles-of-beer.ls-la.net/b.html#Brainfuck

Here's a random number generator:

 >>>++[<++++++++[<[<++>-]>>[>>]+>>+[-[->>+<<<[<[<<]<+>]>[>[>>]]]<[>>[-]]>[>[-
 <<]+<[<+<]]+<<]<[>+<-]>>-]<.[-]>>]http://www.hevanet.com/cristofd/brainfuck/

And a brainfuck interpreter written in Tcl (you can type brainfuck -- or a close approximation -- directly into a tcl interpreter): 

http://www.fishpool.com/~setok/proj/tclbf/

[PT] writes:
And here is a BrainFuck interpreter as a Internet Explorer plugin language - http://brainscript.sourceforge.net/ 

And BF '''is''' a real language - it's Turing complete after all.

Now [Malbolge] on the other hand....