Ask PC Gamer: Should I vacuum my PC?
I know it seems the easy option, but you really shouldn't.
Put the Hoover down. Slowly, now—no one's PC has to die today. Good, now we can talk.
Don't hoover your PC. You'd be better off building a diorama of Dust Bowl-era Oklahoma inside your case and presenting it at a county fair. Vacuum cleaners generate static electricity that could easily mean the death of your system. In fact, get that PC away from anything associated with vacuum cleaners—the carpet, for instance.
It is not the vacuum cleaner's power source that causes a problem. It's the static charge that builds up on the plastic nozzle. Additionally, vacuuming isn't effective unless you hold the nozzle very close to the electronics you're cleaning, so an electrostatic discharge is entirely possible. If you've been vacuuming the interior of your case for ages and have never had a problem, you've been lucky—a quick Google search reveals lots of people who haven't.
There are 'computer vacuums' or 'electronics vacuums', which advertise anti-static features, but they aren't cheap. Spending your hard-earned cash on one is also a little overboard for a task you can get done just as well with a little elbow grease. The cheapest and simplest way to clean your PC remains compressed air and rubbing alcohol, annoying as that can be.
Move your PC somewhere you can easily clean up later and use compressed air to blow out as much dust as you can. If it needs more attention, remove the fans and motherboard and carefully clean them with a soft cloth and 99% isopropyl alcohol.
Or, if you're really lazy, you could just dunk your whole system in a vat of alcohol. You probably wouldn't have a computer that works any more, but it would be clean. (Please don't actually do that.)
One thing you could pick up to help you with this task is an air compressor, or some lightweight handheld alternative. This would help save on cans of compressed air and make dusting your PC an easy task. You wouldn't have to worry about static this way, either.
If you're looking for other computer cleaning tips, here's how best to clean your mouse pad. And here's how to best clean off thermal paste from your CPU. That stuff gets everywhere.