H2 is a terrific database engine. After we solved a problem not related to H2, we switched from PostgreSQL and MySQL (both still supported) to H2. H2 became our primary database choice.
Speed is the main reason, but there are others: the embedded mode is amazing and gives us the flexibility to install the software in a portable device, even share the database on the cloud, let's say via Dropbox!
We don't use many features, because we are "persistent dependent" through "Datanucleus" (no triggers, procedures, etc), but our app is complex enough to push the H2! And it delivers flawlessly.