Regular PC maintenance
Contrary to what some people honestly believe, computers do not need much regular maintenance. Unlike cars or human bodies, computers are remarkably maintenance-free. This is largely because they are mostly electronic circuitry, and circuits last just about forever.
However, if there's one thing in your computer that's likely to fail, it's the hard disk, the only massively mechanical component. This is why backups are the most important part of PC maintence. For your own sake, back up all new data as soon as possible. You've heard this before, but if you're still not doing it, you're just being dumb.
So, aside from backing up, what else should you regularly do with your computer? Mostly just run the standard maintenance software. There are basically four major kinds of PC maintenance software: Virus scanners, disk scanners (like Scandisk), defragmenters, and backup utilities. You should have at least one of each of these kinds of programs, and run them regularly. And speaking of virus scanners, yes, you should update your virus definitions regularly too.
What about physical maintenance? There is none. As mentioned, the computer's circuitry will last almost forever, and the only thing that might fail within the next 20 years is the hard drive. And there's nothing you can do to prevent an HD crash, aside from being gentle with it. (Tip: Don't play football with your hard disk. Bad idea.)
If you really, really want to do something physical on a regular basis with your computer, it *can* be cleaned. The mouse, monitor, and keyboard are all components that can get a bit dirty over time, but they're not usually cleaned regularly. Rather, they're cleaned on an as-needed basis. If your mouse starts moving jerkily, you clean it. Otherwise, it's working fine, and there's no need to clean that mouse until it starts to act up. The only part of the computer you could justifiably clean as maintenance is the interior of the case. The cooling fan(s) tend to suck dust in. This is very rarely a serious problem, but if you're anal, go ahead and vacuum out your case and get the dust out once every few months. It probably won't make any difference to the computer (I know of 10-year old computers which still run fine and have never been physically cleaned), but you might feel better, and happiness is worth any price, right?
To clean your mouse, open it up, get any lint out of the hole, and close it back up. To clean your monitor, rub the screen off gently with a damp paper towel. And to clean your keyboard, get one of those handy-dandy cans of compressed air from a computer store (they're only $3 or so each) and blow a lotta air into it.
Oh, and you might want to get rid of "temporary" files, too. This isn't as big a deal as it used to be, because hard disks are bigger and temp files don't usually take up much space, but once in a while, you might want to check C:\TEMP (or whatever you're using for a temporary file folder) and delete whatever's there. Also, with the uprising of the Web, it's become a good idea to periodically clear your web browser's history and temporary file cache, and perhaps your cookie folder.
Other than that, your computer will probably keep running without any need for regular maintenance. Mechanical things need you to look after them, electrical things (usually) don't. Just let it rip and party on.