Enough people ride fixed-gear mountain bikes that bsnyc has a species name for us: Mountainger.
Here is my converted GT.
Fixed-gear GT mountain bike on Flickr - Photo Sharing!
It's fun in all the ways you might expect. I ride it when I want to make life difficult.
Surly rim and Sun Rhyno-lite rim. Only 32 spokes and I weigh a lot, but the rim is strong, the builder was an expert, and the wheel still spins true.
If your frame has horizontal drop-outs, the conversion should be easy. If its drop outs are kinda horizontal (as with my GT), get a chain half-link and grind flat the sides of the drop-outs. If the drop outs are vertical, either prepare to buy some expensive components or drop the whole idea.
-chris