I wish the games were more like the anime/manga, with events and special interactions with the pokemon you have. Maybe you enter a cavernous place and one of your pokemon decides he wants to fight, and you have to search the cave to find him. Maybe they get angry after losing one too many battles and you have to do x to get them happy and ready to fight again.
Idk, just something to break the monotony of capture the pokemon, level the pokemon, fight the pokemon, ad infinitum.
Make the Pokemon feel like actual animals/little guys/friends. If someone ever does this, they're going to make a fortune, mark my words.