Rapid application development comes to mind.
When I am constantly evolving my schema, I am constantly frustrated by having to maintain the schema in MySQL/SQLite. While I've not done too much with CouchDB yet, I do like how simple it is to evolve the schema during the RAD process.
A case where you might not want to use a non-relational database is when you have a lot of many-to-many relationships; I've yet to get my head around how to create good MapReduce functions around these kinds of relationships, particularly if you need to have metadata in the joining relationship. I'm not sure, but I don't think CouchDB Map functions can call their own queries on the database, since that could potentially cause infinite loops.
