Some great use-cases - for MongoDB anyway - are mentioned on the MongoDB site. The examples given are real-time analytics, Logging and Full Text search. These articles are all well worth a read http://www.mongodb.com/use-cases
There's also a great write-up on which NoSQL database is best suited to which type of project: http://kkovacs.eu/cassandra-vs-mongodb-vs-couchdb-vs-redis
