Rarest stuff you've seen or caught in a Pokemon game

[fenrizz]

In Pokemon Red/Blue you can actually catch Pikachu right at the beginning of the game, on the first forest you enter.

It has a very low spawn, but with a lot op patience it is possible.
I usually try to get him before I move on.

 

[voltman000]

I've played pokemon ever since the red/blue days and have caught a shiny geodude on diamond and a shiny sandslash on white

 

[Magicmad5511]

Shiny Roselia in Pokemon Pearl. Pretty much useless but still pretty cool.
I also once caught a Hetran with a single pokeball. That was surprising.