Yes, external links can hurt your website. For example, you asked some one to provide you with back-links on your website and the person gave you a link which leads to a spam site. Spam site in the sense you run a health related website and your seo guy gave you a link from a website which deals in construction heavy duty machinery, then of course Google will consider this link as a spam because it is not related to your site or post or article that you have posted on your website.
There is one more way of answering your question.. Suppose you and your friend both has health related blog and both of you have done link building on your sites. Some how your friend had his account deleted or did not renew his hosting and his website is not showing on the internet, which means his website is not available. This will lead your link to end up and show a 404 error to your visitors. Google will penalize you for having a broken link on your website. As this link is external and also it is broken link.
Links to a website can have different factors but i wouldn't say it would hurt it unless both sites are neighbouring sites, google analyse the links to determine if you are a neighbouring website and are related to the site in anyway, if you have no relation to the site that links to you and you have no links back to the corresponding website google will only see this as one way which in turn they may not penalise you. if you have links back to the other website and they link to you then google will link both sites a neighbouring website, so any spam could impact on rankings. a good plan of action is if you do not know the details of a website or no idea if its a spam related one you could do a no follow which tells google that you are not related to that outbound link/site.
but as the above posts have said there is many reasons why you can be penalised or ranked higher depending on content, backlinks, linking out, onsite seo and offsite seo all play a part, this also includes who you link exchange with also.
Google do have a lot of tools that can help you too.
If the post you are posting on is related to the topic of your website then it is fine to get backlinks in forum signature but if the content on forum and your website isn't of same niche then I don't recommend getting signature backlinks.
If your backlinks in forum signature on high quality forums then they are quality backlinks and will help to rank your keywords. I have some backlinks in signature on big forums and they are helping reality .