For the DS you have 4th and 5th gens.
>4th gen:Diamond/Pearl/Platinum - Main series games set in Sinnoh, Platinum is the third version, has a lot of improvements over the latter 2 and the only real choice between these three.
HeartGold/SoulSilver - Remakes of Gold/Silver/Crystal, set in Johto and Kanto, they are the same game with differences on the pokémon you find. Check this site for differences between the two:
http://bulbapedia.bulbagarden.net/wiki/Pok%C3%A9mon_HeartGold_and_SoulSilver_Versions#Version-exclusive_Pok.C3.A9mon>5th gen:Black/White - Main series games set in Unova. They are the first games with an improved plot involving the main characters/gym leaders/enemy team/whatever. They have differences between them, Check the pic related.
Black2/White2 - Sequels to Black and White respectively. Plot wise they're not as involving as BW but they have a lot of features BW doesn't have, like improved move tutors, lots and lots of pokémon, grinding places, whatever. They also have differences between them, similar to the differences between Black and Whtie. Check the following site for exclusive pokémon:
http://bulbapedia.bulbagarden.net/wiki/Pok%C3%A9mon_Black_and_White_Versions_2#Version-exclusive_Pok.C3.A9mon 