What is the difference between graph-based databases (http://neo4j.org/) and object-oriented databases (http://www.db4o.com/)?
From a quick browse of both their websites:
The major difference is the way the APIs are structured, rather than the kind of free-form database you can build with them.
db4o uses an object mapping - you create a Java/C# class, and it uses reflection to persist it in the database.
neo4j has an explicit manipulation API.
Neo4j seemed, in my humble opinion, much nicer to interact with.
You might also consider a key-value store - you could make exactly the same free-form database with one of those.