I think of an extended warranty this way. The cost of it is typically less than it would cost to fix the item you're buying it for should it break down. For example, on a $3,500 TV, $100 is not likely going to cover the cost of the piece(s) to fix as well as the installation time for the repair.
As a result, the company selling the extended warranty is saying that they are betting that the item will not breakdown between the end of the Manufacturer's warranty and the end of the extended warranty. If you buy one, then you are betting it will breakdown between the end of the Manufacturer's warranty and the end of the extended warranty.
The company is in business to make money. They are not offering you something that is going to save you money. They are offering you something that is going to make them money. This means more often than not, the item will not breakdown between the end of the Manufacturer's warranty and the end of the extended warranty.
To put a percentage on this, assume that the average cost of repair for your TV is $500. The company is expecting the TV to breakdown less than 20% of the time between the end of the Manufacturer's warranty and the end of the extended warranty. If not, then the company is not making money on this program.
Having said that, if you happen to get a TV that is going to breakdown between the end of the Manufacturer's warranty and the end of the extended warranty then the extended warranty will save you hundreds of dollars. The problem is that the odds are not on your side.
I never buy them and so far I have not regretted it.