I've done all three of the following:
1. Checked a desktop in my full-size suitcase. No problems, but I followed my recommended procedure below.
2. Carried on the guts of my computer in my carryon - hard drive, motherboard with CPU and CPU heat sink attached, optical drive, plus various assorted cables. It got hand-inspected by the TSA but it might have helped that I profile well, have good "TSA demeanor/vibe", and also look sufficiently geeky.
3. Checked a case in it's original box.

If you have the original box the case came in, I'd suggest pulling the hard drive and optical drive (and hand-carrying those), pack the insides of the case with filler, and checking the computer in the original box. I think this is the recommended procedure for the LAN party crowd and is why I have all the original boxes and packaging from my computer cases despite my wife's complaints.