Once I got started on this, I came up with an impressive (to me) list, but impressive in the wrong way. Lotsa planes have needed the brakes bled, so that's not listed here. On the airplanes I've flown / rented:
Rented planes (2000 hours)
* Bad spark plug on first flight after annual, partial power loss;
* Carb heat cable came loose, found on runup;
* Hit a duck on short final at dusk, they made me pay the deductible;
* Vacuum powered DG failure, several in flight. Not sure I've ever had a pump failure, though:
* Flat tailwheel (Decathlon), discovered on rollout;
* Flat main wheel discovered on rollout (Cessna, kept it on the runway);
* Split flap condition in flight. I let the demo pilot land the plane;
* Discovered in flight that both VORs were way out of spec and unusable;
RV-4 (bought) (that one was a real POS but fun to fly) (350 hours)
* Rudder cable came loose from pedals after I changed nylon locknut to castellated to be "safe." My shoe had eventually broken the cotter pin. Discovered in pre-flight;
* Builder mis-drilled the rear spar attach so the plane had a siamesed hole filled with a half-moon spacer;
* High oil temperature because the oil cooler had been mounted against the cowl and there was no room for air to exit;
* Brake rotor came loose from the wheel. Discovered on taxi out;
* Took mags in for overhaul. Knew I was in trouble when the tech said that two of the washers (or something) were upside down, and that they were not resuable;
* Exhaust system failed on takeoff. Too many welds made for a hot spot that failed and part of the exhaust system came loose inside the cowling;
* Navcomm failed, ferried the plane NORDO from Class C to Class D and back;
* Replaced one fuel sender and the dual gauge, but fuel gauges still didn't work;
Cessna 175 (600 hours)
* Failed attitude indicator on a crummy VFR day. Extraordinarily distracting;
* Loose landing gear attach bolt missed at pre-purchase annual;
* Voltage regulator failed in flight. Caught promptly because the ammeter was in front of the pilot;
* Fuel quick drain would not shut off, fixed at Oshkosh by the emergency repair folks;
* All flight control surfaces and horizontal stab damaged in a microburst while tied down and controls locked. I did the preflight entirely out of habit when I didn't feel like doing it, and good thing I did -- the rivets holding the elevators to the control linkage had all sheared;
* High vacuum due to clogged filter;
* Navigational problem due to misprint on a sectional chart;
* One fuel gauge worked well;
AirCam (bought) (100 hours)
* Rotated fuel pickup caused 8 gallons unusable in 14 gallon tank. Two inflight fuel exhaustion events, one in cruise, one on short final;
* Vertical fin mis-installed due to poor illustration in the manual. Repair had the pop rivets installed from the wrong side -- one of them I could pull out by hand;
* Fuel gauges sort of worked, mostly;
RV-8A (bought) (25 hours)
* Had it for less than a year, no problems. When I went to sell it, the buyer's agent asked me what I could tell him about the plane. I told him that he had performed the last annual...
* Fuel gauges didn't work well;
RV-8 (bought) (100 hours)
* Lug on fuel pressure sensor broke off;
* Headset failure (and on other planes);
* An absolutely gorgeous plane, currently for sale;
* Fuel gauges don't work well;
RV-9A (bought) (200 hours)
* Idle set too high, plane barely slowed down on rollout;
* CHT ran high on hot days, attributed to high EGT. Tightened up absolutely everything on the baffles, replaced carb with different model, didn't really solve it, but problem seems to have gone away on its own;
* Throttle would not go in all the way, probably sticking accelerator pump. Discovered before engine start;
* Fuel gauges carefully calibrated but still don't work.
Budd Davisson said that if you have a choice between a used homebuilt and a used snake, buy the used snake. I tell folks new to homebuilts that if they're looking to buy, they better be prepared to deal with all kinds of things.
PS. The RV-4 also had the landing gear seriously toed-out. Pulled the motor mount, had the holes filled in the motor mount and the gear legs, re-drilled in proper alignment. Magnafluxed the motor mount and found cracks, got them re-welded. On the Cessna, had the engine off and also found cracks there. The only welder around was certified but lost his paperwork in a flood. Solution was to magnaflux after the repairs, and that got everything blessed.