If you want to connect JConsole/VisualVM to a remote Tomcat or set up Opsview check_jmx with Tomcat, then you’ll need to enable remote JMX support.
This can be achieved with the following JVM settings in /etc/default/tomcat6 on Debian (line breaks added for clarity):
# Add JMX support
This configuration would typically be locked down with iptables.
For the complete list of settings (e.g. SSL / password controlled access) see the remote section of the JMX guide.