Morris Minor, overloaded with family, flat out on the M5 until the engine seized near Worcester. My uncle let it cool a bit, then took off the head and put it in a stream to cool it down. He thought he knew more about mechanics than he did. Poor car, it wasn't built for that kind of abuse.
A friends Harley Davidson. Rear swing arm broke on one side. Hey, it's a Harley, get used to things shaking and breaking and wheels falling off.
My dads Panther motorcycle, exhaust valve holed. I noticed first a loss of power, and then noticed that one exhaust was glowing red all the way from front to back. The valve was replaced later and the bike was otherwise ok.
Ford Taurus Wagon - about 50 things to list and the car only had 80,000 miles, but the most fun was the steering breaking on an interstate in NJ. The steering let go at speed and felt weird but I was able to drive ok at 65mph. Until I slowed down and all [censored] broke loose. Stopped the car and discovered the steering wheel was only turning the drivers side front wheel. The passenger side wheel was disconnected. Fixed that and sold the car within a week, just glad to be alive.
Cadillac STS. My daughter called me, said the engine overheated, she pulled off the highway. I drove there, and sure enough, the infamous Northstar head gasket problem right on schedule at 100,000 miles. Repair cost exceeded book value of car: from expensive premium car to the scrapyard in only 100,000 miles.
My sons Volvo 740 and Honda Accord, and my wifes Elantra - timing belt stripped. The Volvo was easily repairable, longitudinal engine and not interference. The Honda and Elantra - scrap. The Elantra belt was within mileage and range intervals, not sure about the other two. Lesson - a car must have a timing chain for anything I buy now.
Lots of other mechanical issues along the way, some engine and some not, those are just the ones that came to mind first.