Apache Derby
Apache Derby is a Java based open source Database server engine. It is a very compact and the core engine with JDBC driver is about 2MB only! Derby can be easily embedded into any Java based solution.
Derby has a network server for the engine to be used in client server model. Derby fully supports JDBC 4.0 Spec in latest versions. Derby can also be used in J2ME enviornments.
HSQLDB
HSQLDB is a 100% Java database engine which offers a lightweight architecture. It provides RDBMS facilities with object capabilities of Java. Startup time of database is very low.
Some of the features include trigger support, java stored procedure support, in memory tables, powerful commandline and GUI tools and supports multiple JDKs with switchable code.