From what i understand it's possible but not recommended simply because the parts will not stay as cool as they would in a case, I've seen cases, however, that the parts are basically open to the air around them and they work OK, but they do get hotter then they would in a case, besides that I don't think it would hurt them as long as it wasn't left running, just place the fans close to the CPU and GPU and you should be ok
(pretty sure it would work, but up to you if you want to try it)
hmm, would be the same as just placing it on your desk really, which would be awesome as well lol, but ya running it without a case, the only real danger is heat, but if you put enough fans on it you should be good until you get a case for it
while these are way funny, and there are alot more pictures on the web of hackjob cases, you have more to worry about then heat. One wrong touch and you zap something dead with a static discharge, believe me done that.
Pony up the $50 for a plain jane case to protect your new investment.