The most important part of your laptop that needs to be clean is the heatsink. Yes, heat is the "cause of death" for most laptops. The heat not only causes all components to expand and contract a little (as you turn it on and off), but will also reach dangerously high levels and make your laptop crash or shut down if the fan(s) and the heatsink(s) are clogged with dust.
All computers work a little bit like vacuum cleaners, sucking air form one side and blowing it out from the other. Unfortunately they don't come with filter bags to catch all the dust and debris. After just a few months the fans and heatsinks are well coated with dust. If not cleaned, their effectiveness quickly drops and eventually goes down to zero when the heatsinks get fully clogged.
The Fix? Get yourself a can of compressed air and blow away the dust off the fan and heatsink. USE SHORT BURSTS - AVOID HYPER SPINNING THE FAN. It is also recommended that the computer is completely shutdown. This has to be done every couple of months or after about 50 - 60 days of using your laptop. The compressed air is quite handy for the keyboard too, blowing away all the debris from between the keys. This is not a very well known fact, but it is the most important part of maintaining your laptop.
However if the heatsink has already been clogged, this won't help. The compressed air will not be enough to unclog it. If you have never cleaned the heatsink and you had used your laptop for over a year, chances are that both the fan and the heatsink are clogged with dust and debris. The solution in this case is to remove the heatsink, clean it and install it back. This is best done in a laptop repair shop, as it takes quite a lot of experience and dexterity. One slip of the screwdriver may kill the laptop!
Another cause of overheating could be due to the thermal paste between the processor and the bottom of the heatsink. This can also be fixed by a laptop repair shop if necessary.
Another good overheating prevention is to ensure that the rubber feet on the bottom of the laptop are intact. Unfortunately they are usually just glued to the plastic and tend to fall off quite easy. They are very easy to replace and are available as spare parts for most laptops.
And lastly, don't use your laptop while it's on a soft surface, like bed cover or sofa. That will block the fan and the laptop will overheat. Try using something with a hard surface under the laptop, like a large hardcover book or a tray.
Simply put, heat is the biggest enemy of all laptops. By maintaining the cooling of your laptop at peak efficiency, you are doubling its lifespan.