How useful would amateur radio be in a true SHTF world?

I'm not talking some temporary or localized emergency—such as a hurricane or flood. But in a really bad, perhaps lasting for years, real grid-down situation.

It doesn't matter how it happens: EMP attack, nuclear war, continent-wide natural catastrophe, or simply a massive societal breakdown due to any variety of causes. No cell phone service, no Internet, no commercial radio, no delivery of supplies of any kind,— nothing. Basically back to a medieval existence.