Path finding
AI for none local enemies
Persistent world stuff
One world shared between multiple people
There are lots of things that don't require instantaneous response in a game.
The only real criteria is that the cloud have data available, and the computational cost be relatively speaking large compared to the result packet size.
You could do all of that with your own services today though, it's just not worthwhile.
Having said that, it won't be ubiquitously used unless it's free and it doesn't cut out a lot of your market.
The more interesting things to me is the possibility of persistent state when not playing, allowing interaction potentially from other devices.