Pokemon Stadium (N64): Red/Blue/Yellow
Pokemon Stadium 2 (N64): Gold/Silver/Crystal/Red/Blue/Yellow
Pokemon Colosseum (GCN): Ruby/Sapphire/Emerald/FireRed/LeafGreen
Pokemon XD (GCN): Ruby/Sapphire/Emerald/FireRed/LeafGreen
Pokemon Diamond/Pearl (DS): Ruby/Sapphire/Emerald/FireRed/LeafGreen
Pokemon Box (GCN): Ruby/Sapphire/Emerald/FireRed/LeafGreen (only Ru/Sa can be played on tv however)
And is there some other DS game that can transfer Pokemon from the GBA games? No
Ranger maybe? Manaphy can be transferred from Ranger to Diamond/Pearl
And between the 2 colosseum games, they both have different obtainable legendaries, Colosseum 1 has Raikou/Suicune/Entei/Ho-oh, while Colosseum 2 has Articuno/Zapdos/Moltres/Lugia, and both games have move tutors that can teach certain moves, like Self Destruct to Snorlax or Mewtwo.
EDIT: the game in the picture appears to be a Yu-Gi-Oh! game, heh