The possibilities are kind of limitless. Redis implements a lot of data structures beyond a simple k/v map.

A simple non-caching example, but we use it for distributed locking, more specifically a distributed countdown latch. This is much cleaner and more performant (for us) than doing a similar operation in a traditional RDBMS.

Another very common example that is used in a lot of tutorials is maintaining a leaderboard using a sorted set.