I\'m used to using relational databases like MySQL or PostgreSQL, and combined with MVC frameworks such as Symfony, RoR or Django, and I think it works great.
MongoDB was featured on FLOSS Weekly this week - http://twit.tv/floss105
A database using a similar concept is CouchDB which was featured on another FLOSS Weekly: http://twit.tv/floss36
I think it's worth listening to those in addition to the links provided by @marcgg