There's been a lot of work in this area lately. Amazon SimpleDB uses a similiar "non-relational" database model.

Personally I haven't gotten into them at all. It took me years to think in 3rd normal form, so even if I used one of these databases, I'd still end up with different tables and having primary and foreign keys.

So all these would accomplish is moving joins from the database layer to the application layer. And I already have enough work to do at the application layer.