I have a fixed rear wheel that I throw on the back of any bike I've just gotten and haven't had the time to get the deraillers up and running.
I think it's a nice way to get to know a frame, see how it feels on it's own without all the fixins to obscure and complicate it.
Inevitably I get around to putting all the gears on but it's kind of fun to try them all out that way first.