If you came to the point of being ready to start a new project, here are few links to some cloud based APIs to consider:
1. StormPath - quite good a user management and you get free perks as well.
2. Mandrill - if you need a good notification (email based) system. Again, quite a decent free of charge limit.
3. MongoLab - well, that's MongoDB. And if you don't know what it is by now, then you shouldn't worry about it at all (caught your attention? Google for it then). Free 0.5Gb instance is a good starting point.
4. Google Chart API - Not the best one, but it's free and quite ok(ish) for building dashboards.
5. GeckoBoard - a better dashboard API, with HTML5 support (WebSockets and all that stuff), not for free though ...
And of course, you can test all that with Amazon for free for one year.
This is it for now, I will do my best to keep this list updated.