I have a few genealogical mysteries. They bug me because in my family we rely a lot on family lore--as a kid I used to get so bored listening to all the grown-ups repeat stories about "dead people" over and over again. So it seems like we ought to at least have some hints about these people, but no, it's like there's a brick wall behind them.
1) My great-grandfather, that's pretty recent. My dad knew him. I'm like, Dad, didn't you ever say, "Grandpa, tell us about your parents and siblings"? Allegedly he had a sister, but no one knew anything about her, like her name; and his parents' names are unknown. As an adult I can track him well, but not as a minor, and thus I can't get back earlier.
2) Farther back, but our "illustrious founding ancestor" who had a million offspring. I can track him easily from about age 25 onward, but no one knows anything about his parents or siblings.
3) My great-aunt, my (late) grandfather's sister. He had several siblings and all of the others are neatly documented. This one sister married a guy, moved to Iowa, and had five kids. That's all I know. His name and her name are both super-common, and I don't know the kids' names. I've probably stumbled across records of them, but I have no way to verify which family is them. And no one I ask seems to know any more. The wilds of Iowa, from which there is no return...
On a totally different topic, I sometimes see things on the street and wonder how they got there. Like a shoe. Under what circumstance would you lose a shoe, and just leave it there?