SQLite is a popular small SQL database that runs on almost all platforms. It has almost become the standard database when building Windows 8 store apps. (Of course, other alternatives exists.) Is has also good support in Windows Phone. Two .NET APIs exist to work with SQLite in .NET, SQLite-NET and SQLiteWinRT.
In this dev.cast I talk with Andy Wigley about SQLite. He has done a very good session at TechEd Europe 2013 called Support Your Demanding LOB Apps With SQLite and Windows Phone 8, that I recommend.
Windows Azure Mobile Services with SQLite Data Sync for Windows RT and Windows Phone Using Portable Class Libraries (Nick Randolph MVP)
Posts on SQLite-NET: