Often, especially in a forum such as this, people leave backlinks to websites that are not related to their site's content. Is this useful? Is a dofollow backlink with proper anchor text from a site that is not related better than no backlink at all? If so, what are the pros/cons for doing this? For instance, in my signature there are links to my site, but it has nothing to do with SEO. Does this hurt my backlink to the point that my signature is hurting my sites's SERP and PR?
It is a matter of opinion but I am pretty sure most would agree that there is no penalty from building backlinks from a site that is not related to yours. Instead you are just not receiving as much benefit as when you post on a related site. The benefits you are receiving is another backlink which search engines do count and it has a keyword anchor text which they count as well. They just are not giving you as much credit as when the site contains content related to you. So a suggestion is to find forums that relate to your topic and post on them as well as this one.
yes i agree with Jon Potts...related back link can help you give some new traffic but non related back link can help you keyword ranking in SERP.
It counts, but not as much as links from related websites. Why? Because this forum does not have "authority" in your search terms and your backlinks are not surrounded by content related to those keywords. Just as an example, how much credit would you give to the opinion of an "expert" on Rembrandt in a forum discussing gardening? Same with search engines.... As Jon indicates, post in forums related with your topic, the effort is the same and those links will count more...
Nope your signature won't hurt you. I have seen a site that ranks #1 with all his links having nothing to do with his niche. Although if you get relevant backlinks Google will love you for it.
I think it's no problem with your website, when we participate in forum signatures are needed, it's can not be good for Search engine but everyone will know you!
I'm finding this site surprisingly relevant for my site, because of all the non-native English speakers here (I'm sure you would have noticed them ) Your sig on the other hand ... there's not that many people on this forum who just had a baby, I imagine. I had a baby a few weeks ago and do have a flubby tummy at the moment so I had to have a look
It will not harm your SERP. But in this case there are less chances to increase the ranking of your website in search engines. There is no any problem if you are giving backlinks to non related sources. You may get visits but not targeted visitors.
search engine like only quality backlinks and it doesn't matter that back links related to your website or not.