Went to a great talk about Neo4J at their London offices last night. It was great to hear (new to me) ideas about how to store data.
If I were to sum it up in a really short amount of words I would say that it is somewhat like an RDBMS but instead of joining tables you define relationships and those are stored at insertion/update time instead of query time for a RDBMS via SQL. Being able to do arbitrary joins between tables in an RDBMS may be hugely useful sometimes but mostly we're thinking about objects, so it seems to be a good trade off, perhaps it will help get us away from the scourge of ORM's... As a side note these relationships appear to be much quicker than SQL joins.
Definitely one to watch out for