I have a few sites using "SQLite":http://sqlite.org as the database. SQLite is nice to use because the database is contained in a single file on the file system. This means you don't need to have a daemon running, you don't need to setup user permissions on the database, and backing up is a breeze.
Unfortunately it turns out there is a nasty bug in the blog software I use, "typo.":http://typo.leetsoft.com Typo tries to execute a nested transaction but causes the system to crash as nested transactions in SQLite are not possible. That said, I'm not sure why this error is fatal. I can't say I have looked deeply in to the problem, but I knew there was a problem as every few days my sites would go down. I have since switched to the more widely used "MySQL":http://mysql.com database and everything is much better.
A fortunate side effect has been that I've noticed a more responsive interface. SQLite is very fast as a read only database which I thought was great considering a blog is mainly a read system. It turns out that Typo stores session information with-in the database there by squashing any benefits gained from using the high performing SQLite.
Don't use Typo with SQLite - they don't mix well.