MongoDB is the new no-SQL database which offers more flexibility and efficience than the traditional SQL databases. It's free, easy to use and install (JSON based), prepared for replication (HA) and sharding.
Here is good tutorial to start with:
This is also a good tutorial from 10gen (The guy behind MongoDB)
From the web page of Mongo, there is an interactive shell which could be used to play with the data.
(Press on the "Try it out")
The official web page offers really complete information.