No doubt you have noticed that stores tell you the computer comes with a 90 day warranty or a one year warranty; and for a fee - they will sell you an extended warranty. There is always a chance you bought the lemon made on a Monday. However, assuming you don't get the lemon (which would manifest itself while still on standard warranty) you don't need the extended warranty. Remember you have the standard warranty period to get even the lemon fixed. The best protection you can buy for your computer is a line isolator for the power input and the phone line. In most cases (if your computer breaks; and it is out of warranty) it will be the modem or video card or even a memory module. These are all things you can go buy and replace yourself; probably for less than that extended warranty.
Laptops are a different subject all together. If the LCD panel on the laptop burns out - it can easily cost you more than the laptop did. I once did a time and material repair on a guys' laptop that was out of warranty. It cost him nearly $1,100.00. Obviously, you can buy a nice new machine for that much money. But, if he had the extended warranty; it would have cost him nothing. Laptops are unique in that you almost always have to go to the manufacturer to get parts which means prices are not competitive.
I did not buy the extended warranty for my desktop. However, I did buy the extended warranty for my laptop. Not only that. But, I bought the accident protection that Dell offers for my laptop. Because it is at high risk. It is not always sitting on my desk at home. If I drop it and crack the case, Dell will fix it. Or if someone spills coffee on it and shorts it out, it is covered. So for me it seems like a good deal to buy the extra protection for the fully loaded laptop. For a more basic laptop I would say put the money for an extended warranty aside and use it to buy another basic laptop when the old one breaks.