When to choose checked and unchecked exceptions

Question

In Java (or any other language with checked exceptions), when creating your own exception class, how do you decide whether it should be checked or unchecked?

My inst

Answer 1

The rule I use is: never use unchecked exceptions! (or when you don't see any way around it)

There's a very strong case for the opposite: Never use checked exceptions. I'm reluctant to take sides in the debate but there seems to be a broad consensus that introducing checked exceptions was a wrong decision in hindsight. Please don't shoot the messenger and refer to those arguments.