There are two concerns I have with carpet:
1) Having the PC close to the ground results in it getting dirtier faster, since the fans will suck in dustier air closer to the ground. Carpet is also notoriously dusty.
2) The possibility of electrostatic discharge damaging the PC, caused by walking on a carpet and then touching the PC. I would say this is fairly low risk, since if you touch the PC case it should ground you and prevent you from damaging any internal components.
That being said, I (and I'm sure many others) have had several PCs on carpet for years without any problems.