They aren't considered a powerful link from a site source for the simple reason that a site owner can link to themselves, every time they post from the forum.
It's often said in threads pertaining to pagerank and the like that posting on forums and weblogs will improve search engine ranking. This is where there seems to be a failure by a lot of people to understand the distinction between gaining a benefit on search engines and gaining with respect to relevant traffic.
With the comments above there is a confirmation that there is little, if any, benefit in using forums specifically for the purpose of improving pagerank or search engine position. What might
be gained is some relevant traffic, if the signature function on a forum is, where permitted, used to include a link to a site with the site's title, as per mine. If, for example, someone is interested in antiques and wants to look at a site with hundreds of pictures of them and happens by a link to such a site they are likely to follow that link. Obviously this is more likely to be the case where suck a link relates to the site it is on. EG: If a link from this website points to a web directory or similar resource it is more likely to get followed than a niche antiques website.
Technically they are only limited by how often they can comment in a day. Many people, particularly the worst elements of the internet, have the most time on their hands, because they don't have jobs or other concerns. So they can build up 10's of thousands of posts on forums, which all create links.
Imagine someone posting 50,000 times on a forum and gaining all those links, and them all counting strongly in the search engine.
It's a case of do something silly often enough and people will get sick of it. These days robots have all but taken over the role of junk-posting though there's cases where a real person will do the job themselves.
This has lead to great improvements in the ability of forum software to defend itself against stupidity. Many forums have a variety of features to slow people down, one good one is where people are limited to only a certain number of posts per hour. This is where robots shine. People don't have the patience to play the waiting game whereas a robot will just keep attempting to post until the forum lets it. Let's hope that some day there is an additional feature to block this as well and perhaps one to block cross-posting. The latter is probably easier to achieve.