MongoDB fills our more traditional database needs. We knew we wanted Trello to be blisteringly fast. One of the coolest and most performance-obsessed teams we know is our next-door neighbor and sister company StackExchange. Talking to their dev lead David at lunch one day, I learned that even though they use SQL Server for data storage, they actually primarily store a lot of their data in a denormalized format for performance, and normalize only when they need to.
Used to be MySQL, but once moved to MongoDB, everything just speed up dramatically, data became pretty and easy to work with. Sophisticated aggregations allow us to run complicated analytics anytime as easy as possible.
Nearly all of our backend storage is on MongoDB. This has also worked out pretty well. It's enabled us to scale up faster/easier than if we had rolled our own solution on top of PostgreSQL (which we were using previously). There have been a few roadbumps along the way, but the team at 10gen has been a big help with thing.