The amazing little SQLite database engine now officially supports Windows 8 Metro style applications. It sounds like this was done with the full endorsement of Microsoft so you should have no trouble including it in your Metro style apps and get the blessing of our friendly Windows Store custodians. I believe this covers Windows Phone 8 as well. Here is the news:
SQLite version 3.7.13 adds support for WinRT and metro style applications for Microsoft Windows 8. The 3.7.13 release is coming sooner than is usual after the previous release in order to get this new capability into the hands of developers. To use SQLite in a metro style application, compile with the -DSQLITE_OS_WINRT flag. Because of the increased application security and safety requirements of WinRT, all database filenames should be full pathnames. Note that SQLite is not capable of accessing databases outside the installation directory and application data directory. This restriction is another security and safety feature of WinRT. Apart from these restrictions, SQLite should work exactly the same on WinRT as it does on every other system.
Thanks D. Richard Hipp!