Question

Can you catch shaymin in any Pokemon game?

Answer 1

No.

Shaymin is an event exclusive Pokémon only.

The only game which you can get Shaymin in legitimately is Pokémon Platinum at the Flower Paradise. Although this location can only be accessed with Oak's Letter which is a Key Item that was only obtainable through a Nintendo Event. The Event has long since past.

Source: http://bulbapedia.bulbagarden.net/wiki/Shaymin_(Pokémon)

Hope I helped :)

Comments

"Although Oak's Letter is present in the game data for Pokémon Diamond and Pearl, the item was never distributed for those games by Nintendo. A Shaymin could be caught on those games by acquiring Oak's Letter via cheating, but, due to the fact that Pokémon Diamond and Pearl does not apply the fateful encounter flag, it would never be able to achieve its Sky Forme."

Answer 2

No. It was only available at Flower Paradise in Gen IV, as an event Pokemon.
Gen V and Gen VI will need to migrate it from Gen IV.
All games before Gen IV, obviously, cannot receive it.

Hope I helped. :)