Just the collecting, slowly completing it but also getting more 100% IV pokemon and more elite gym pokemon.
Breeding could be cool, if it is done correctly and in a way that makes sense. For example, if you breed a 90% IV pokemon to a 100% IV pokemon, the resulting IVs should be between 90% and 100%. All the values of the offspring should not be random, but taken from mom or dad.
New pokemon in the wild would be nice, we got a few new pokemon, but they seem quite useless and you only get them from eggs, and i had no luck yet.
Shiny pokemon would be cool, even if its just optics.