Extended Warranties are a highly personal decision. As others have said, they are significant money makers for the dealerships, so odds are, you won't recoup the premium in claims paid.
That being said........ You need to look at your personal situation, both financially and your view on risk avoidance. If a $3k - $4k repair bill will cripple you financially, do you want that dead truck sitting in your driveway, while you continue to make payments on it?
May people will suggest putting the premium in the bank as a "rainy day" fund, but for many people, that's easier said than done.
In my lifetime, I've purchased EW's only twice.
First time was when we bought our used Monaco Executive. We had no previous experience with a big DP, not real knowledge of how well it had really been maintained. I knew a replacement engine or tranny would run 5 figures, so we bought an EW for 1 year. After that year, once we had a better feel for what we had, we did not renew.
Now, I bought my 2015 Jeep Wrangler brand new ~~18months ago. I purchased the Mopar lifetime warranty for it, after much thought. Reasons I jumped at it are:
FCA's poor quality reputation.
Wrangler's excellent reputation for holding value.
My expectation that I'll keep the Jeep long term.
I have coverage forever, until such time as the repair cost outweighs the KBB value of the Jeep. At that time, FCA will cut me a check for the KBB value and the warranty ends. Bumper-to-bumper, $100 deductible. I just could not pass that up.