My reading of history often turns up some interesting trivia, and US Presidents are a good source for this kind of thing. Here's one I just encountered about a future President meeting a former one:

Herbert Hoover was shortstop for his freshman baseball team at Stanford, and he later served as student "manager" for the team. When former US President Benjamin Harrison attended a game, he was seated without having to buy a ticket. But when Hoover realized this, he asked the former President for his twenty-five cents admission. Harrison paid Hoover; wouldn't that coin have been an interesting collectible!

Benjamin Harrison is the only President who was the grandson of a former President. His grandfather, William Henry Harrison, was the "Tippecanoe" half of "Tippecanoe and Tyler too" of the 1840 campaign, but served only one month before becoming the first President to die in office.