While using my Troy Bilt Lawn Tractor I heard a loud pop and the engine died. When I tried to start it again, the flywheel just freewheeled with no resistance at all. The engine is a B&S Intek 18.5 HP OHV. An inspection of the engine didn't show any oil leakage or other apparent problems. I'm thinking (hoping) that the key on the shaft was sheared off. Am I dreaming or do I have a major problem?

Well, I think you probably are not dreaming, the flywheel key is either sheared, or the crankshaft would have to be broken, and I seriously doubt that. I would say that it is the flywheel key sheared.