NoSQL systems such as MongoDB are those which are designed for incredibly data-intensive applications - Facebook for example created a NoSQL solution called Cassandra to handle the vast amounts of data they had. NoSQL is useful for those who are building highly scalable applications and helps to reduce the need for empty table columns by not enforcing a database schema, so for instance if you had a table in which you stored information about your friends, you wouldn't have to include the reading interests of one where you knew the reading interests of the other.
Relational databases do have their place, however NoSQL isn't really meant as a replacement, just as a different way of approaching the idea of data storage on a large scale. I would say that in the future more and more companies will begin using NoSQL solutions, but at the moment most people with small websites simply don't have need of a system designed to deal with such quantities of information.
Hope that helps!