Generation is determined by the core mechanics behind it. These change drastically in each generation. Each generational shift comes with new Pokémon and in each generation a slayer is born.
Generation I;
Green, Red, Blue, Yellow
Generation II;
Gold, Silver Crystal
Generation III;
Ruby, Sapphire, FireRed, LeafGreen, Emerald
Generation IV;
Diamond, Pearl, Platinum, HeartGold, SoulSilver
Generation V;
Black, White