The db4o series (that is one gnarly URL!) on developerWorks is intriguing and easy to read. I didn't know anything about db4o before reading it, but the first article starts at the bottom level. db4o is an object database specifically oriented toward Java and C#. It's designed to eliminate the object-relational impedance mismatch by...tossing out the "relational". Save an object. Retrieve it. According to the articles, db4o certainly meets the goal of higher developer productivity.
I'm still skeptical about how it compares to the usual SQL databases in several ways: storage efficiency/data duplication, performance, security, scalability. It was also interesting to note in the later articles that db4o faces some of the identical difficulties as ORM tools: lazy loading, inheritance hierarchies, collections of collections (of collections of collections), refactoring, mutually-referenced objects. As an object database closely integrated into code, db4o has distinct advantages when confronting these difficulties, though. The fact that every object has a unique ID automatically probably helps a lot.
For a new application (greenfield), db4o might be fun to try. Where I work, all the data that matters is stored in "legacy" keep' em-running-til-they-croak language-agnostic databases, so db4o isn't an option. Not without a messy bridging/replication layer, in any case. Software that makes data integration much easier is software that can conquer the world.