Reading about the batted ball hitting fallen helmet spot on got me to thinking of the weirdest one I ever saw. Rules don't matter; this is pure Serlingville.
B1 hits sharp liner to F1. The sphere hits his glove. In chronological order.
a) glove flies off.
b) ball heads directly skyward.
c) glove lands on ground.
d) ball (I swear)
lands in glove.
e) F1 sticks hand in glove, holds it up with ball, which never touched terra firma.
Since I am a man of constant truth, I must admit I stood, mouth agape

... and made no call. But, praise be the specter of Nestor Chylak, B1 just stood there. F1, smarter than all of us, threw to F3 for the out, which was signaled by my mouth-also-agape partner. Then a beat. Then gales of laughter from all involved, including fans, B1 and his coach.
Flame away for my not giving the "no catch" mechanic. Hey, I was much younger; at least I didn't signal the out.
Your turn, gang. First-hand stories only, no urban legends.
Ace