You fail to obtain Pikachu in Yellow version
You lose against the Poochyena (Or Zigzagoon, depending on the version) chasing Professor Birch in R/S/E
You waste your Master Ball on a level 3 burned Caterpie with a sliver of health left
You fail to catch that Caterpie with the Master Ball (There's actually a screen of someone catching a nearly-dead level 40 burned Loudred in the Emerald guide on page 114)
Every Pokemon Teleports from you, or uses a suicide move like Selfdesctruct... and you have a Pokemon preventing them from running out and the Pokemon you're trying to catch isn't even supposed to know the move ("OMG, RATATTA!" *Rattata uses Selfdestruct* "Oh, darn...")
You hatch a Pokemon egg and it turns out to be rotten
All your Pokemon faint... at the title screen
The Pokemon Center offers a price to heal your Pokemon... 100 yen more than you have, everytime
You try to go up Cycling Road on a bike and the guard doesn't let you
You Surf on a Pokemon and then it knocks you off and swims away
You trade a Pokemon, and the Pokemon the other trainer trades comes out of its ball, looks at you, screams, then goes back to its original owner
You tell your Pokemon to use Cut... and it turns emo on you and Cuts itself
That's all I could come up with for now