In general, I agree with everything that has been said about extended warranties for vehicles and other things.
That having been said, I personally have had multi-thousand dollar payouts on two different vehicles that essentially put me in the black for on such policies for my entire life. On at least two other vehicles the cost of the policy and the avoided cost of repair were roughly comparable.
The two vehicles with big payouts were a 1991 GMC conversion van with should have been a "bulletproof" Chevy 350 V-8 and the other was a 1991 Honda Accord station wagon. The engine in the van suffered from an undetected manufacturing defect which resulted in accelerated wear of the entire engine. On the Honda the dealer determined that the transmission had failed even though it wasn't exhibiting and noticeable symptoms. In the two cases, the full cost of replacement by a rebuilt engine and transmission were covered by the warranty.
I recognize that this was purely bad luck on my part, but it sure was nice not having to pay the repair bills for those two major repairs.
As cars get more complex the chances of expensive failure increase. Even small repairs can be expensive. Last year our nearly indestructible 2014 Honda CR-V developed a crack in the A/C evaporator. It was "kind enough" to have had this failure just before its 6-year, 100,000 mile service agreement expired. The ~$1200 avoided cost of the repair was just slightly less than what I had paid for the coverage. Not a bad deal IMO.