Catching a friggin' Chansey was always a pain in the butt.
Not only was it extremely rare, you couldn't battle it with pokemon, it would flee after one turn, and half the time the dang safari ball would miss it anyway.
I never caught one in the original games, my first Chansey was in Silver I believe.
Others:
- beating Brock with Charmander/Pikachu
- Rock Tunnel without Flash
- trying to catch Mewtwo after using the Masterball on something inconsequential
- Seafoam Islands puzzle
- Not being able to fly straight to the entrance of Victory Road if you faint inside
- S.S. Anne sailing away forever
- 9999 coins for Porygon, I mean wtf