I've killed JMS in all our projects, AMQP is much more reliable and also works across the board across a large number of languages, not just on the JVM like JMS does with some great other features you don't get in JMS.
Where to use it? Everywhere you can where it makes sense to do so.
Need to send an email? Throw it on the queue, now it's no longer your application's responsibility and another application that deals only with email can pick up the email and send it. Need to register a user, throw it on the queue, let the accounts application register that user for you. Need to update account details? Throw an UpdateAccountDetailsRequest on the queue. Need to get a list of all stock that has not been sold? Throw an UnsoldStockRequest on the queue and wait for an UnsoldStockResponse from the queue.
With AMQP you get the further benefits of exchanges ... need to notify all applications that they need to refresh their cache? Send a RefreshCache request to a fanout exchange and all applications will receive the RefreshCache request. Want to get notified every time an error occurs in any of your applications? Throw all the logs on the log queue and add a subscription that listens for error messages on the log exchange which will forward you all error messages to you application in realtime.
When building a Service Orientated Architecture, every action you do becomes a message you can throw on a queue. The nice thing about this is that you get to decouple your application pieces to a point where all you need to know is where the queue is sitting and what format the message needs to be that you want to send. I don't care how that email is sent, as long as it is done - my way of getting that email sent is simply by throwing an EmailRequest with the content on the queue and my code can continue without caring how it is done or who does it or when it's done.
Read the book Enterprise Integration Patterns, it's packed with predesigned solutions that all requires some sort of message queue whether it's AMQP, JMS, TIBCO, MSMQ, etc