I have had three occasions (two at the previous house) where I was very glad I had a service contract with (originally) Minnegasco and (now) HomeSmart. They treat a non-functioning furnace past November or so as an emergency, and every time the furnace has been promptly repaired -- though one of those times it meant the repair person came back with the necessary part at 1 am.

I'm not a big fan of insurance or service schemes in general, but this type has been worth the money for the convenience and peace of mind.