Which databases support redistributable filesystem storage?

Which reasonably mature relational or NoSQL databases support filesystem storage that can be moved with the application (probably as a DB file and driver)? I woul开发者_StackOverflow中文版d like to try Couch or Mongo, but I am not sure they support it.

I need this for a pet project. Would like to learn something new (preferably NoSQL, not SQLite).

After some more research I discovered I can find a good deal of information googling for embedded databases.