While debugging and testing locally, though? They're extremely useful.
I think they're also useful in production code, although much more rarely. I've had a few times when a customer is having a strange problem that higher log levels helped to quickly resolve.
Being able to have them enable the higher log levels, reproduce the issue, reduce the log level to normal, and send you the logs can occasionally find an issue that would have taken forever to track down otherwise.
And that's not even to mention special processing. In the unices, anyway, the log daemon can take different actions depending on what level the log message was issued at. CRITICAL errors can result in automatic notification to a dev, for instance.