Pokemon started on the original Game Boy in 96 with Red/Green (Red/Blue in the US, in 98). Just about every generation of Nintendo's handhelds has at least one generation of Pokemon.
Game Boy has Red/Blue, and Yellow
Game Boy Color has Gold/Silver, and Crystal
Game Boy Advance had Ruby/Sapphire, Emerald, and FireRed/LeafGreen
Nintendo DS has Diamond/Pearl, Platinum, HeartGold/SoulSilver, Black/White, and Black 2/White 2
Nintendo 3DS will have X/Y once October rolls along
That's just covering the handheld RPG series; there's a bunch of Pokemon games for Nintendo's home consoles spanning from the N64 era to the Wii.