Installing a Database - Snorby/snorby GitHub Wiki
Snorby is working on an eventual migration to mongodb. But for now, you are still given the options of at least Postgres and Mysql. Oracle and Microsoft SQL Server are options. If you've used them, please feel free to tell me about your experience.
An open-source database under GPLv2 license, often considered the most widely used.
Claims to be the most advanced open-source database. It has it's own license called the PostgreSQL License (http://www.opensource.org/licenses/postgresql), which seems to be very liberal.