When is shared hosting no longer enough?

At what point would you move a site from shared hosting to a VPS?

Regularly hitting a resource limit seems like a good reason. Needing custom software is another. But moving just because a site feels slow could leave you with the same problem and a server to maintain.

If you’ve made the move, what pushed you to do it—and did it fix the problem? Interested in the extra maintenance work as much as the performance difference.