Depends, what game are you playing?
In R/B/Y, You could find Mewtwo, the other legendaries, complete the pokedex, Lv.100 your pokemon, etc.
In G/S/C, Beat Red, complete the pokedex, Lv.100 your pokemon, etc.
In R/S/E, You could beat the contests, rematch the gym leaders, collect soot xD, explore underwater, and areas like Shoal cave, beat Steven, complete the pokedex, Lv.100 your pokemon, etc.
In D/P/Pt, Beat the contests, they have that place that is to the far right of the map, I can't remember what it's called xD
complete the pokedex, Lv.100 your pokemon, etc.
In B/W, You can find the Seven Sages, play the musicals, complete the pokedex, Lv.100 your pokemon, etc.
and I haven't played B2/W2 xD