I’m looking to buy a late model used car and would like to get an extended warranty/service contract to cover the next few years.
I think the only reason to buy any insurance is to cover an extraordinary cost that a person could not otherwise afford. Keep in mind that insurance is about the only business that makes money by not providing the service being sold, and that the only thing insurance insures is the profit of the insurance company. Go back to my first sentence.
Wife and I have only bought used cars beginning after 1986, the year of our last new car. We have relied heavily on Consumers Reports and the reliability and repair records of used cars. Except for a Chev Celebrity wagon many years ago on which we got an exceptional deal, we only have bought used Toyotas (there are other high quality used autos, we're just partial on this), none from dealers, all from private parties, with the most mileage at our time of purchase being 186,000. Based on the purchase price and not counting gas, oil and normal servicing, no car we have purchased has cost us more than $0.10/mile to own, that is, buy for $12,000 / $0.10 = minimum number of miles we should be able to get out of the car = 120,000, and every used car we have owned has done much better than this.
We also have never followed the recommended service interval, except religious on oil and filter changes every 5,000 miles and tire rotation at the same time. Typically we bring the car in for service about every 90,000 miles. Oil/filter/rotation I do my self. We have only had one break down, that being a timing belt failure while I was on my way to bring the car in for a timing belt change and other service.
My recommendation is to buy a quality used car, take care of it, and skip the extended warranty. There should never be an engine or transmission failure. I feel that if a car can't last at least 250,000 miles without any major repair, it is not worth buying.