- HSQLDB - Used by OpenOffice, tested and stable. It's easy to use. If you want to edit your db-data, you can just open the file and edit the insert statements.
- H2 - Said to be faster (by the developer, who originally designed hsqldb, too)
Which one you use is up to you, depending how much performance and how much stability you need.
The developer of H2 has put up a nice performance evaluation: