"cloud" is a very nebulous term in any case.
Exactly. In this particular case, I am mainly expecting it to be a web service of some sort. Either through an API with the standardized XML expectations, or through an old-school url-parameter system.
From an app-side, I'd like to not care what platform/language/toolset my app is running on ... it should be able to talk to the system. This would open up the possibility of having the game be available on a variety of systems (iOS, android, Windows, etc.) and players would be able to interact with each other without knowing/caring what piece of equipment or OS you're running on.
From a server-side, having a connection-free, web-driven solution would be nice in that it could be hosted by anything that can serve up web pages, and port 80 is rarely blocked ... keeping tech support issues on the user side to a minimum.
This would only work for non-real-time games that can save true "game state" info.
... Dicey Curves, Space Mission, Jump Gate, Gem Raider, DareBase, Castle Danger, Keeps & Moats Chess