My first reaction is that a fixed mountain bike would be super irritating to ride and almost dangerous. After thinking about it more though, it seems like on the right trail like the ones in Edmonton like 65'er mentions or in FKMTB07's pic it could be a ton of fun. Learning another way to control the bike is never a bad thing in mountain biking so if you weren't bashing into stuff all the time than I bet it could turn out pretty well.
On tech trails though? F-that. Give me a freewheel. If I can't place my pedals just so I'll bash 'em cornering and anywhere remotely tech. No way I want to compromise that much.