In conventional PCs, the fan for the power supply (PSU) pulls air out of the unit, meaning it gets in via all the little cracks and gaps, etc. This is not good for things like CD/DVD drives etc. and the power supply itself.
If you're careful, you can open the PSU and re-mount the fan the other way round, so it sucks in. If you then organise a filter outside the case (J-cloths are pretty good for this, the bigger area the better), you can keep a slight positive pressure inside the case, stopping dust getting in through all the little gaps.
I did this successfully years ago with a video edit suite in Nepal - the airborne dust was in danger of knackering the video heads and tapes. PCs in comparison are far less vulnerable, apart from DVD, tape and floppy disk drives. As long as the dust isn't conductive, or highly static-charged they'll work for ages in inches of the stuff without problems, provided they continue to be adequately cooled.
We used to keep parrots as pets, free-flying around the house. The first time I opened my PC case after the first one arrived, I had a bit of a shock: Charlie used to sit on my shoulder whilst I worked and preen herself. The PC case was about 1/2" deep in fluffy grey feathers. After that I got into the habit of hoovering the PC out every six months or so. Apart from one screeching parrot during the process*, there were no other side effects.
Cheers,
E.
*Hoovers are, apparently, seen to be competition for parroty affection. Charlie always used to yell her head off whenever we were using the hoover, which wasn't fun when she was sitting about 2" from your ear!