A couple years ago Consumer Reports did a report on "extended warranties," and after pointing out that even the extended warranty companies are in business to make a profit (which used to be possible on the interest earned on premiums paid before claims were settled, but no more while nobody's paying interest because rates are so low), they concluded that the rare individual who came out smelling like a rose while everybody else essentially wasted their payment made extended warranties a bad deal. The only exception to that was the Applecare warranty on Apple products, which they concluded was OK because of the excellent service provided.
We bought a new-to-us used car last year, and of course, the offers of extended warranties are still coming in from far and wide. We were quoted $6,500 for two years and an additional 50,000 miles above the factory warranty. If that car even looks like it'll cost us $6,500 to fix during that period, we'll unload it in a hurry as a lemon.
Of course, you need to think about it a bit. But do recognize that whatever premium you are being asked to pay has to represent a profit to the insurer. You will only do well should a catastrophic problem arise. As in all things, you pays your money and you takes your chances.