If your usage of the database is quite low and your server can do its own locking (i.e an exclusive lock of the whole database whilst saving some player stats), then I might recommend SQLite.

There are a few java bindings knocking around like: http://code.google.com/p/sqlite4java

SQLite is cool because it is very easy to migrate between servers and does not rely on sockets so your game server can access it directly (obviously this means you want the SQLite database on the same server).