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....