I guess the three that stick in my mind are...
1.7 morris Ital estate (yes I know!)
Had the car for about 2 years, got through about 6 or 7 gearboxes in that time. they used the same gearbox on the 1.7 as they did on the 1.3 and it simply wasn't strong enough for the larger engine so it would blow out the idler shaft for first and reverse on a regular basis. Not a huge problem seeing as gearboxes where easy to come by in scrap yards at the time and cost £20, I got it down to under 2 hours for a gearbox change on that car. (driving about with no reverse gear for a few weeks every few months was always fun!)
Mk1 Fiesta 1.3 supersport.
For some totally unexplained reason this car kept breaking clutch cables and it always managed to do it at the most inconsiderate times and places! luckily new clutch cables were only about £12 so I took to carrying a spare and could change it in about 3minutes even in total darkness by the time I got rid of that one.
Mk2 2.3 ford Granada.
Bought the car with a knackered cooling system on it but otherwise seemed fine, replaced pretty much the entire cooling system (rad, pump and most the pipes) and it run lovely, for about a week until the distributor shaft sheered and dropped itself down into the internals of the engine. didn't cause any damage but would have required an engine lift and full bottom end strip down to recover the shaft!... it went to a banger racing team.
Other than that I've been pretty lucky with most my cars and I've had loads (probably about 40)