Here is a good article that talks about the needs that non relational databases fill: http://www.readwriteweb.com/enterprise/2009/02/is-the-relational-database-doomed.php
It does a good job at pointing out (aside from the name) that relational databases arent flawed or wrong, its just that these days people are starting to process more and more data in mainstream software and web sites, and that relational databases just wont scale for these needs.