I've had so many amazing uses for JMS:
Web chat communication for customer service.
Debug logging on the backend. All app servers broadcasted debug messages at various levels. A JMS client could then be launched to watch for debug messages. Sure I could've used something like syslog, but this gave me all sorts of ways to filter the output based on contextual information (e.q. by app server name, api call, log level, userid, message type, etc...). I also colorized the output.
Debug logging to file. Same as above, only specific pieces were pulled out using filters, and logged to file for general logging.
Alerting. Again, a similar setup to the above logging, watching for specific errors, and alerting people via various means (email, text message, IM, Growl pop-up...)
Dynamically configuring and controlling software clusters. Each app server would broadcast a "configure me" message, then a configuration daemon that would respond with a message containing all kinds of config info. Later, if all the app servers needed their configurations changed at once, it could be done from the config daemon.
And the usual - queued transactions for delayed activity such as billing, order processing, provisioning, email generation...
It's great anywhere you want to guarantee delivery of messages asynchronously.