I don't remember a most embarrassing thing, but AN embarrassing thing...although nobody saw.
Unfortunately, some of the pairs of pants I have do tend to slip down when I'm walking, even when tied up. And although I don't wear them often, there have been times where I've had to hold my pants up in the middle of, say, carrying in firewood from outside.
Now I dunno about you, but that's embarrassing to me to think if anybody saw that. ><