I did buy an extended warranty for one car, never had a warranty claim until it broke down with only about three or four months left on the warranty. That one paid off.
In another car (same mfr) I looked into getting one when the regular warranty was about to run out. Sales guy looked and said: main thing that happens to these older cars is X and Y and you already replaced X so it's not worth it. I always wondered if what he really meant was "main thing that happens is something expensive and I'd rather get paid retail to fix that". Either way I skipped it and never had a problem.
I do consider it insurance.