I used to build Ruby on Rails apps with MySQL.
MongoDB currently become more and more famous and I am now starting to give it a try.
The problem is, I don\'t
I don't know much of the underlying theory. But this is the advice I got: only use MongoDB if you run it across multiple servers; that's when it'll shine. As far as I understand, the NoSQL movement appeared in no small part due to the pain of load-balancing relational databases across multiple servers. So if you're hosting your application on no more than one server, MySQL would be the preferred choice.
The good people over at the Doctrine project recently wrote a quite useful blog post on the subject.