I do computer repair as a 2nd job. About 2 months ago, I got one in from a fella who complained that it wouldn't come on anymore. When I opened up the case, there was so much dust clogging the innards I couldn't even see the parts anymore - just vague lumps where the hard drive and motherboard should have been. The power supply was completely caked and was fried from overheating.
Take a few minutes once a month or so, remove the case and blow it out with some canned air. It will extend the life of your computer considerably.
I know what you mean. We have 3 cats. Every hair they shed seems to get sucked in there. I was planning to put some kind of filter on the last computer I built, but never got around to it.
Adding air conditioner filter material to the air intakes will also help reduce the amount of dust getting into the computer. At the very least, it cuts down on the cat hair.