One thing that bothers me:
In the majority of fangames, people don't edit the Pokemon's stats/movepool/abilities etc. Making it almost identical to playing the official games. Just a few changes could make a game a lot more interesting. Heck, even just changing the Pokedex entries or move descriptions would make a game more fun to play for me. (It actually seems like something new that way)
Some other things I like to see are:
less linearity; Multiple routes to get through a town, an increase in fieldmoves (HMs) so there are multiple ways to get through a cave or something.
I'll post more when I think of other things.