While I would say the Missingno glitch, which frightened me as a child to the point of me having something of aquaphobia for years after, I can't.
Because, in my old copy of Blue, I never got that far thanks to Safari Zone. I'm serious; little kid me was never able to get to the old guy's dentures because he got lost every time. And never had his Pokemon learn Strength. And by proxy, never got the HM for Surf.
Older me wishes little me had a strategy guide like he did for Pokemon Silver. >=(
EDIT: Also. Lieutenant Surge's Gym. Darn those trashcans. Little kid me didn't know the mechanics of how the puzzle worked, and took forever to get to Surge.