Disclaimer: I have no practical experience with MongoDB at this point, so if my assumptions below are wrong, then please let me know.
I can see MongoDB as an ideal database for serving Write Once / Read Many website content, for example Amazon or New York Times Online. It would clearly be superior to ASP.NET + SQL Server, where data for a webpage is queried from relational tables on demand and then transformed into HTML just in time. The same goes for persisting online shopping carts in MongoDB.
However, I would have serious doubts about it's suitability for a line of business application like CRM (due to lack of data integrity constraints) or for data warehousing (due to limited support for aggregate queries and indexing).
Also, because MongoDB is a document centric database that contains data as serialized JSON or XML, I suspect that it would less suitable than a RDMS database for data that is frequently appended or updated. In other words, if you update a MongoDB document, perhaps something like adding additional office visitation records to a patient's chart, then the change of size operation would require that the updated document be re-written to a new physical location on file. I'm thinking here about fill factor, page splits, and fragmentation.
"Do not seek to follow in the footsteps of the wise. Instead, seek what they sought." - Matsuo Basho