I put a link to my site in my signature on several discussion forums (like this site http://forum.northernbrewer.com). Google webmaster tools is reporting hundreds of link from these forums. These forums are un-related to my site. Are these links hurting me?
yes, un-related links can hurt you. What you can do is, you can disvow un-related baclinks from your webmaster tool. Do it slowly and monitor your website accordingly.
Most forums, I think, are nofollowing their links these days, whether they are in signatures or blog posts. When found in forums whose topics complement your own, they may still lend authority to your site. When the forum's content is dissimilar, they probably won't and could have the (unlikely) potential of doing harm. I would simply change my signature in these forums, which should change the signature on all of your past links in the same forum, and not worry about it anymore unless I had reason to believe that a penalty had been applied.
Yes, obviously. If you use an unrelated link which do not look natural then that can hurt your website.