The list of reasons why a computer can overheat is quite a few. Making sure these problems are dealt with is important to keeping a computer healthy. It would be like a person ignoring a cold and letting it develop into the influenza virus when it is as simple as washing your hands. Keeping dust out of a computer is important but not entirely practical. Dust, hair, and other small particles WILL make their way into a computer. Once a month, or whenever you see your computer covered in dust, you should clean it out. Important things to remember are that the components inside of a computer are fragile. To clean them, use a dry paper towel - not a wet paper towel, and not a wash cloth. Using a dry paper towel insures that no moisture reaches those electrical components, and fuzzy residue does not get left behind inside the computer from a wash cloth or dish towel.
Lightly wipe the components to remove the dust. Having a vacuum hovering over what you are wiping is also a nice idea as long as it is a safe distance away from the computer. Hitting a computer with a vacuum is never a good idea.
While dust is the most easily fixable annoyance concerning overheating computers, you also must make sure you have enough circulation. It does not matter if your computer is sparkling and dust-free, the more power your computer has, the more heat it is going to exert. One way to combat this is to make sure enough fans are installed in your computer tower. What is "enough"? The average computer does not need more than one tower fan and one CPU fan to adequately cool the system. Also, pre-built computers are designed with cooling in mind, so unless they screw up, a cooling system should have already been placed with-in your computer capable of cooling it efficiently.
Other factors become important, though, when you upgrade something in your computer.
A new graphics card, for example, might make the computer run at a higher temperature. An added fan might make the transition easier for the computer to manage. If you upgrade a CPU, take careful consideration when picking out the heat sync and accompanying fan. If you upgrade the CPU and not the fan that goes with it, you could possibly end up with a broken computer because it could not handle the heat of the new processor. A good indicator of an overheating CPU is starting up your computer only to see that it shuts off within a few minutes (or seconds if it is really hot). You cannot just say, "slow computer, fix yourself." Actions need to be taken to cool down your computer.