When is a message queue more than just a buffer?

We usually think of message queues as a way to separate services and handle lots of requests all at once. But sometimes, I see them doing way more complicated stuff, like coordinating things or even being the main way important services talk to each other. So, when do you all figure a message queue is good enough for more than just buffering, and what makes it right for those tougher jobs? Are there certain situations or patterns where how reliable it is matters more than how fast it can send messages?