None, zero. The closest I had was a nearly new Ninja 1000SX - it didn't have any *real* problems but the clutch was so noisy it sounded like it was broken (it wasn't). And the factory oil filter was on so tight it could only be removed destructively.
I can say this though - as a purveyor of the GTA's finest used motorcycles, a fair number of problems I experience are caused by people "improving" their bikes. And I think I've had like... two bikes ever that didn't come with toasted batteries. Hence my battery post in the tech section. Second most common problem is people re-using crush washers and ripping out the threads on the drain plug / cracking the oil pan.
Question for OP: have you ever had cause to remove the wheels from your Gold Wing?