I've tightly integrated it with my work's educational platform (proprietary so I can show it off... sigh).
Other's I've seen recently are:
http://www.bigblueplanet.com/
http://www.jnuke.com/
(Apologizes to any I missed).
The level of integration depends on the amount of work you want to do. Simple integration is just a matter of getting some sort of of SSO to work so that your users will automatically get Jforum users.
Tight integration gets into making user info a combination of your apps's user info and jforum's user info; integrating your Applications' groups with jForums's group model; and optionaly creating some admin interfaces that match your apps better.
The places to start are the SSO sections in the Documents and the various threads here. Then dive into the DAO implimentation code to really get a feel from how user and group info is populated.
Along the way, you will eventually need to look at the template files to hide features you don't want or generate different URL's etc.
And BTW, one of the goals of jForum 3 is to look at making integration easier. But that's not even in Alpha stage.
[originally posted on jforum.net by monroe]