> something that the developer didn't think to test at all.

Raising hand, guilty as charged. I test for things based in my concept of how the system works, but those darn users may have other ideas!

Actually, when I found a user who seemed to have a knack for finding bugs, they were gold and I let them know I appreciated their efforts.

> unit tests should be used to baseline something after it ships

That has not been my experience. I found that unit tests let me get the pieces working properly so that when assembled, the chances that everything worked as expected were much improved.