IMO an extended warranty plan is never worth it. Especially in the beginning. Your bumper to bumper and emissions should give you peace of mind till close to end of those. If you save money out of each check during that time you will have a nest egg saved for maintenance and repairs that will be better than the fine print coverage of the warranty plans.
It depends.... We got one when we bought our new Vette many years ago. One repair we had to have done (bad brake booster and contamination in the system) after the factory warranty had expired, covered more than the cost of the plan. Granted, it wasn't much more than the cost of the plan, but we did come out on the positive side.
I will also say that the GM plans cover a fairly wide range of stuff. Better than a lot of aftermarket plans. It is also real easy to file a claim under a GM plan, unlike some others.
In truth, it is crap shoot. Kind of like auto insurance. You pay for something you may never use. In essence, you're banking on something going wrong with your car after the factory warranty runs out. On some models, and in years past, maybe that wasn't as likely. With the complexities in most newer cars, that picture may be changing some... More can go wrong and repair bills are generally higher. It is an individual choice.
In our case, we bought one for the Vette for piece of mind and the knowledge that Vettes do have "quirks" that can pop up from time to time. The cost of the plan wasn't that much comparatively, so we took a chance.