I am developing a Java Desktop Application and want a light database
that can be used with Hibernate
and that can be packed with an application.
JavaDB (Sun's supported distribution of the open source Apache Derby), HSQLDB (not very active) and H2 (the successor of HSQLDB) are all 100% Java embeddable database engines and can all be used with Hibernate (i.e. there are dialect for them). Refer to this page and this one.
HSQLDB has the smallest footprint (~700 KB) of all of them. But feature wise (see this comparison), H2 is the clear winner and its footprint (~1 MB) is still smaller than Derby's one (~2 MB).
The final choice depends on what you need but H2 is a good compromise of features and size (in other words, a big competitor). Have a look at the mentioned comparison.
Another Alternative would be SQLite.
Hibernate and SQLite
I would recommend HSQLDB. It is small and fast and runs fine with Hibernate. Hibernate has a dialect for the Derby DB as well (haven't used it though and I think it is not officially supported by Hibernate yet).
You can also try Firebird
There is an embedded version and a client/server mode version
Here an link to hibernate supported database