Following on from my posting about DB2 Express-C, I was very interested to read an article comparing Cloudscape/Derby with MySQL. Cloudscape is a slightly different product to both DB2 Express and MySQL, since it can be embedded inside your application and doesn't need any specific administration tools. The database is hidden from the user. This can be a huge advantage, depending on your application requirements.
For example, in WebSphere Message Broker version 6, the Configuration Manager now uses Cloudscape instead of DB2 to store its information. This means that it is easily portable (it now runs on all of the WMB supported platforms), and you don't need to install and use DB2 if you don't want it.
Take a look at Cloudscape, also known as Apache Derby, if you are interested in a lightweight embeddable database. If you need something a bit bigger and don't mind some administration, DB2 Express-C is worth a look.