When should you move on from using just one database?

We've all been there, right? Your main application is humming along, but the database is starting to really slow things down. Could be too many writes, sluggish reads, or honestly, the data is just getting too huge to handle. Besides just making copies for backup, when do you know it's time to actually change how the database is set up? Like, when should you think about breaking it apart, using different kinds of databases for different jobs, or moving some of the data to its own service? What are the first signs that things are going south?