When you want to do many small real time operations against your data. The model fits well with most web sites (the unit of work for a given request tends to be quite small). Loggin also comes to mind as does some basic geospatial work. I think for most cases it does what a RDBMS can do but with less friction (you'll still use an ORM/ActiveRecord, but it'll be a much more lightweight).

Why don't you check out mongly.com/tutorial/index and get a quick feel for it?