If you want to just play with JMS on your local computer, you could start with Glassfish from Sun. It will pretty much "just work" out of the box.
Yes, you get the full boat JEE app server and stack as well, of which JMS is but a component, but at the same time it's trivial to install and get working. Especially if you add in NetBeans as the IDE, since it's well integrated with Glassfish.
That said, you certainly don't need an entire JEE app server just to use JMS. There are many JMS compatible Messaging servers available. ActiveMQ is a single example.
I only suggest Glassfish because it has a great out of box experience in terms of download, install, start up and it's running.
If you want to work on configuring another option, there are several.
Also, I suggest Glassfish (or any full JEE server) simply because even if you're just interested in JMS, you'll likely find that the JEE Message Driven Bean (MDB) model actually works pretty well as a mechanism to leverage JMS. And it, too, is pretty simple to set up for the basic use cases. Once you have an MDB, you might want to talk to a database, and the JEE server has connection pooling, etc. built in already as well. You also get transaction management with JEE (which can actually be important with JMS).
Basically, while JMS alone is interesting, the other services are also compelling, even if you "don't need them yet". If you want to dabble with them, they're readily available in a full JEE server, which promotes experimentation, and perhaps adoption.
So, starting with a Glassfish download can actually be an interesting door for learning and discovery things above and beyond JMS.