In CouchDB, Map/Reduce is the primary way that you access the database. The first time you access a "view", it will do a Map/Reduce on the entire database. On subsequent access, it will redo the Map on new records. To make this work, the action of the Map function needs to be immutable with respect to the record; this is intellectually pleasing but incredibly annoying in practice.
I haven't really used the Map/Reduce functionality of Mongo yet, but I have poked at it a little. Basically, with MongoDB, you do a one-time transform from one "collection" of records to another. It doesn't automatically update the way CouchDB does, but I can do things like joins that I couldn't do with CouchDB.
Once again, Mongo's practicality makes me happy, while Couch gives me reason to admire but avoid.