Celebrity interviews often ask that. I am no celebrity, but I do comment on the pathetic banality of celebrity interviews.
I was at a sports centre where we played five-a-side football. After the game I took off my kit and glasses, picked up my towel and stepped out of the changing room which had one door leading out to the shower area and another back out to the gym's reception. Obviously (because otherwise I would not be writing this) I stepped through the wrong door.
It's perfectly true, as a few colleagues from the football team and a slightly shocked receptionist can testify. But it was not really embarrassing, even at the time, it was just funny. However it is one of those anecdotes that is easy to regurgitate if ever asked to "reveal your most embarrassing moment".
Actually real embarrassment is when you simply say slightly the wrong thing in a social situation, the premise of the best British comedy of the decade. Real embarrassment is not when you make an honest mistake, it is when you do accidentally reveal a personal prejudice. But you don't admit to those.