Non-caching things I regularly see people do with Redis:

- Rate limits for API endpoints via the leaky bucket algorithm

- Feature flags and stats tracking

- Websocket pub/sub

- Background job queue

In general, lots of things that need to survive deploys (so they can't be in-memory in the app) and/or they need to be coordinated across multiple horizontally scaled servers and/or things that prefer to be in a data structure which is slightly awkward to stick in a database table.