I've had a car in which the O2 sensor died, because I was told it was going to cost quite a bit I didn't get it replace. Anyway's biggest problem I had was that the exhaust coming out of the engine was extra hot and turning the exhaust pipe coming out of the manifold blue. Finally it stressed out the bolts holding the pipe and manifold together, letting the exhaust leak into the engine compartment.
Just so you don't get worried, this didn't happen overnight. Probably closer to a 3 or 4 month period.