A warranty is insurance against the replacement cost of a product. Every consumer product has a lifespan, either the time it will take before it fails, or the time it will take until it's no longer of any value to you. You probably won't be using the same computer 10 years from now. Your fridge will probably last 15. Other household appliances, maybe 15-20 years. At some point they're going to break or become obsolete. Researching the products you purchase, either the specific product or the quality control history of the company that produced it should give you an indication of how long the product will last before it needs repairs or replacement, and how much it's going to cost over its lifetime to maintain.
Now, how much does that warranty cost? Chances are good it's going to cost somewhere around 20% of the purchase price of the product. This is only a good deal if the product is EXPECTED to break within the next 5 years. Note that it won't protect against obsolescence, only replacement/repair of the original product. Of course, the next question is, why would you WANT to purchase a product that is expected to fail in less than 5 years? Therefore, if the product doesn't need the warranty, you shouldn't buy the warranty. If it DOES need the warranty, you shouldn't buy the product.
So what happens if that new TV dies 2 years in. You're out the money, right? Well, yes, there is a statistical chance that some consumer products are going to fail before their average expected lifespan. It happens. However, it's a low chance, and if you purchase 20 different products of relatively equal value, 1 of them might die before their time. So purchase 20 gadgets worth $500 each one of which breaks halfway through its lifespan, then out of $10000 worth of purchases, you lose $250. Extended warranties on all of those products would have cost you $2000, and the warranty period is still unlikely to cover the whole expected lifespan of the product. You could just as easily purchase your own "extended warranty" by putting 10% of the value of the product into savings at the time of purchase, and over the lifetime of all of your products you can expect to use maybe half of it.
Warranties start to make sense (maybe) when you're purchasing a single large purchase, with large repair expenses and pseudo warranty savings with other consumer products won't be sufficient to make up for it. Something like a car or purchase of similar magnitude. Again, if you purchase 20 cars at a time (probably only if you're a business), warranties probably no longer make sense as repair costs over ALL of the vehicles is likely to be less than the price of all of the extended warranties.
So, in summary, for something really expensive, yes. For anything reasonably less, no.
-Restil