Redis is particularly useful for implementing simple message queueing systems where the full functionality or power of something like RabbitMQ is not required.
For example, when parsing incoming data into a database, push incoming data onto one end of a Redis list, and have a seperate worker process popping them off the end and into CouchDB, MySQL or whatever.
The fact that Redis list operations are atomic mean that multiple worker processes (possibly on seperate physical boxes) can process jobs simultaneously.
Result: the internet is entirely decoupled from both the hard drive and the database, and extremely high performance is possible.
Twitter Streaming API, anybody?..