Small Cloud Database
If you are strictly interesting in


setting up a quick-and-dirty database
free to use and setup
not worrying about a lot of administration
not being tied down to Storage Engine configuration/tuning specifics


then I would recommend the Xeround Cloud Database service.

I just wrote a post about Xeround's limitations in terms of MySQL and its configurability. Since that is not a concern, Xeround gives you a fairly easy Database to setup and tools to manage it. You can literally create a Xeround MySQL Instance in under 5 minutes.

The free service will give you room to create a 10MB DB. If you need slightly more space, there are pricing options.