When should you really start thinking about using a distributed cache?

We've all hit that point where the database is just slow, you know, latency spikes and all that. We've put in local caching where it made sense, but now we're wondering: when should we actually bring in something like Redis or Memcached? What are the big signs or problems that tell us it's time for that kind of system? Are there certain ways we access data, or specific kinds of data, that just beg for a distributed cache?