Java 5 has a built in JMX container with about 5 or 6 mbeans that give general information about the JVM. Earlier J2SE platforms does not come with a built in JMX container.
As for
J2EE...
Weblogic has a built in JMX container, with about 300+ mbeans on start, instrumented to monitor every aspect of the system. This number of mbeans will increase for every session, user,
servlet, ejb, etc. that gets added.
JBoss is about the same -- in numbers but different from Weblogic. In fact, JBoss is one big JMX container. The Servlet container, EJB container, etc., are just mbeans running in the JMX container.
Tomcat has about 30 or so mbeans on bootup -- most of them are of a "generic" nature. Not really explaining this one well, except when I was working with it, there wasn't much interesting.
I have Websphere on my work list. And one of these days, I will get a customer that needs it, and I can bump up the priority on working with this one...
Henry