Collecting structured log data like monitors or exception traces or user analytics. Lots of documents, no fixed schema, they're all self-contained with no relations. Map reduce makes query parallelism crazy magic.
A content management system. Some stuff may want data from across relations (who owns this thing, and what is their email), but that's pretty infrequent and having nice flexible-schema documents that contain all relevant information that's being CRUD'ed simplifies things hugely - particularly in MVCC systems like Couch that put stuff like multi-master/offline-online sync and conflict resolution in the set of core expectations.
Edit: That said, Postgres is also MVCC, and hstore makes schema an option the same way that relations and transactions were already, so I think it could do pretty well. I haven't gotten the chance to play with it in recent history, unfortunately.