I've had it happen from a dodgy magneto in a 152 on a trial flight. Fortunately we were on the way back anyway so I just made sure we took the route with lots of fields and didn't tell anyone until I'd got rid of the student.
The scariest one, though, I was unaware of until the next day. In a Warrior, ILS BKN050 2500m vis +RA. The aircraft purred. Next day we discovered two cracked cylinders!
Now I have two nice turbine engines and all the redundant systems in the world. But I'd kill to earn this salary on a light single / twin.