from a development standpoint only, I like the fact that I don't have to write database migrations (as defined in Rails). It means I can iterate more quickly during the development.
As well for data aggregation kind of jobs (such as http://www.toutpourmonipad.com/ where I munge different-formatted data streams), it's really convenient to be able to mix datas that are partly equal, partly different, when it's relevant to you.
Edit: forgot to mention that MongoDB comes with a built-in geographical index (MySQL doesn't have it, I'm not sure for PostGres - I believe it's via some extension).
Edit2: forgot to mention I really appreciate the upsert abilities for what I do (http://www.mongodb.org/display/DOCS/Updating#Updating-Upsert...)
Edit3: anyone with some curiosity for MongoDB will appreciate this book: http://www.amazon.com/MongoDB-Definitive-Guide-Kristina-Chod... - well-written and concise
For basics, the Little MongoDB Book (http://openmymind.net/2011/3/28/The-Little-MongoDB-Book/) is a bit dated at this stage, but a good starting point.
Finally, there are free MongoDB courses available at http://education.mongodb.com in various flavors of programming language, as well as an ops/DBA focused course.