Your mouse is a wonderful device, serving as your gateway to interaction with the graphical user interface of today's modern operating systems.
Your mouse is also a delightful little crud magnet. Each time you move it, it picks up dust, lint, hair, or any other particles that are on the surface below. Over time, this will cause the mouse to become unresponsive or unusable. Cleaning your mouse regularly will prevent it from becoming sticky.
There are two main types of mouse; mechanical, and optical. They can be easily identified; a mechanical mouse has a rubber or rubber-coated steel ball visible through a hole in the bottom. An optical mouse either uses a bright visible LED and sensor to detect movement over a textured surface such as your mousepad, or a special mousepad with lines on it (these are true antiques!)
If you've got an optical mouse, all the cleaning you should have to do is just to wipe or blow the dust off of the sensor window(s) on the bottom. Also, you'll want to wipe off any crud which has formed on the little feet on the bottom.
A mechanical mouse can be trickier to clean. The first thing you'll be doing is removing the ring on the bottom that retains the ball. This is usually accomplished by turning it in the direction indicated by some arrows on its surface. After you've done this, knock the ring and ball off into your hand and look inside. You'll see three or more rollers, each coated in cruft. Using a Q-tip dampened with alcohol, scrub this rubbish off. If it's too difficult to remove while working through the bottom hole, you can remove the one screw holding the top of the mouse on and disassemble it further for cleaning. Once the rollers are clean, reassemble the rodent and you're ready to go.
If your mouse is seriously misbehaving, such as moving only straight horizontally or vertically, the opto sensors inside may be obstructed by dust. In this case, opening the top of the mouse will be required. Remove one screw opposite where the cable enters (it may be under a label) and unhook the top from the bottom up near the buttons. Inside, you'll find two slotted or perforated wheels at the ends of the rollers, which move through a black plastic U-shaped holder containing an infared LED and sensor. Clean this area out by manually plucking loose the dust bunny or blasting with compressed air. Reinstall the top cover of the mouse by hooking it back together at the button end and screwing it back together, and you're done.
Don't remove the top of a mouse while it's in operation; there's a risk that you may fry something in the mouse or PS/2 mouse port if you cause a short circuit inside, in addition to that of just b0rking the mouse. Oh yes, before I forget to say this -- make sure that while cleaning your mouse, your computer isn't in such a state that you can accidentally click something truly destructive.