Most devs don't need the power of sharding, which is why that benefit can never be felt. But the reality is this is probably the #1 characteristics (huge benefit) of NoSQL databases. Google and Amazon definitely paved the way for this movement, primarily b/c they dealt with tons of data. Its simply cheaper to scale out (distributed) than scale up.
You can't aggregate data with a relational database. But you can aggregate with (most) NoSQL databases (exception is graph dbs). Instead of building relationships, with NoSQL you're building composites. The huge benefit here is enabling sharding while, having your data all in one place.
Lastly, a relationship db is made up of tuples and sets of tuples. With a NoSQL DB you can have complex data structures. I think this is the point you we're trying to make re: Documents.
I still love relational databases. It's cool to have options though. Before, relational was the only way.
The question is how do we determine which db to use (or use more than one)? Ah, the beauty of polygot persistance...