Think that your forums and the loose, user-generated content generated there is bringing your whole site down? Gary Illyes says that this is "unlikely" to be the case.
Peter Parker makes a nice case in the comments. The initial question to Illyes was about "light content." Parker writes, "I've had a situation where the forum was a cesspool of people sharing porn links...and the threads began ranking for porn terms. So maybe there are instances where forums can hurt the site."
I agree with that - but in order for forums to get that way, they have to be almost completely unmoderated and barren of attention. If you're not paying attention to your forums and taking care of them, then yes they can become cesspools and come back to bite you.
There's also a very bitter person in the comments because "boo hoo Google made all the forums start sharing nofollow links so I can't get traffic and juice from them anymore."
Anyway. If you have a section of your site that has user generated content...just show it some love and give it some attention on the daily. Or, if you can't do that, don't have them. That's my opinion anyway.