Which one is recommended depends on your requirements. You won't go too wrong with mySQL, postgressql (or however you spell it) or sapdb.
Holy wars aside I recommend sapdb for production (IMVHO). It's a bit of an investment to get it going but once you do it just keeps running.
What about the hypersonic db that ships with jboss ?
What vendor is that ?
umm hypersonic has changed a few times. I think you can get info as HsqlDB from sourceforge.net. It's certainly open source but not sure which is the active development these days. It's a nice fast little db but I wouldn't recommend it for anything serious in production, just quick testing.
I personally couldn't be happier with anything other than MySQL. Since version 3.23.50, it has supported every feature I could want in a database using InnoDB tables. This includes foreign keys and constraints, as well as ACID transactions. It is easy to install, setup, administer and proven trustworthy in production by such popular websites as Yahoo! Finance and Slashdot.org.