As explained best in Wikipedia, Apache ActiveMQ is an open source message broker written in Java together with a full Java Message Service (JMS) client.
It is the most mature implementation out of the three that we examine here and has a long history of successful production deployments. Commercial support is offered by many companies including Red Hat.
It is a fairly simple queuing system to set up and manage. It is based on the JMS client protocol and is the tool of choice for Java Enterprise Edition systems.