I was wondering....everyone mentions that we should get other popular sites to link our website, which will help in promotion and PR rankings. What if that popular site had a forum and I posted in the forum a message and referred to my www website. My link would now be on that popular ones site when it is indexed, but not on a links page. Does that hold as much as being on a links page or do crawlers know a forum page from a links page?
You should always use your anchor texted link in forum posts (if possible). The effect is weak, but better than nothing at all. IMHO a link on a links page is better, just as long as there aren't too many outbounds on that page (over 30).
What you are suggesting is a well known technique - to post to other forums with your forum URL and anchor text in your signature. If you post to lots of different forums, it's a great way to get free backlinks on a wide variety of domains. It works even better when the forums use mod_rewrite to have the appearance of static URLs (such as DaniWeb does) so the pages with your link get indexed well. It's one of the best ways of link building with the primary downside just being the time it takes to find lots of various forums and to register and post to each one of them.
As far as links on a link page, as Promediacorp has suggested, those are actually one of the worst types of links to get because it's very easy for Google to tell what is a links page (even if there are just a set few links on it). Google is even known to give less weight to links that are on pages that contain the word "links" in the URL such as a links.html page!
Links built into page content, however, such as forum signatures do, are the best way :) Anytime you can get a link built into page content, go for it!