#1 for me has always been a persistent state Pokemon MMO game. Pretty much every feature in that game lends itself perfectly to this format. Chansey, for instance, is supposed to be incredibly hard to catch, hence the name. But with individual carts, anyone can walk around until they've caught one, so its not really rare at all. In a persistent state world, they can actually implement a true "rarity" among certain pokes and items. If you've ever played a persistant state MMO game, you know that collecting and showing off rare things is the TRUE driving force behind them. In addition, not everyone would have to be a trainer. Perhaps you make your money raising signature pokemon (there's a system where by completing a quest or having a rare item, you can raise pokemon with a special move they can't get normally or with slightly higher values in a certain stat) and then selling them to trainers, and eventually save up enough money to buy a bigger house/training place and stock it up with rare collectible master ball Christmas tree ornaments or something. Or you could run tournaments in your own gym and have people sign up to battle you using your own custom rule sets and environmental modifiers. If they win, they of course get to show everyone the badge that you designed. The turn-based nature of combat lends itself well to management of different connection speeds.
Basically, the good opportunities in such a game are limitless.
What's not limitless is patience when dealing with a bunch of younguns running around demanding, in horrible, near indecipherable terms, that you give them a shiny pikachu. If there was a way to keep the n00bness in such a game to tolerable levels, I think I'd give my left nut to have this game.
And I think one is in development, but a Cowboy Bebop game could be pretty cool. Now, I know that licensed games rarely deliver the goods, so I'm not sure what to think of the upcoming CB game. The story of that series, and the action elements, would have been great to have been exposed to first through a game, but it'll probably disappoint after having seen the series first.