while relating to a different sites from your site, you necessarily have a decision on your hands. Should you add a 'rel="nofollow"' attribute to the HTML anchor tag used to link to the third-party website, or should you leave it out (do-follow it) .
In the eyes of the search engines, a do-followed link of your site is basically a voting for the site being linked to. In a sense, you're vouching for the legitimacy from the site you're linking to. If that site turns out to be abusive, you risk hurting your site's credibility with the search engines by linking to that site.
Then again, linking out to superiority sites that are related to the subject matter of the page you are linking them from, is known to really benefit your site. As long as you don't overdo it, most search engines revalue your letting them know that a site is worth linking to, and will give your site a little more believability as a result. If you no-follow links to high-quality sites and pages that have content that is related to your site's content, then you're basically telling the search engines, "I can't be bothered to check that this site is worth linking to, but I'm going to link to it anyway.", which obviously doesn't encourage the search engines to have confidence in either you, or your site.
Naturally, it's not always possible to thoroughly vet each and every site you may link to on your website. There's also the possibility that a site may change for the worse (or for the better) after you have visited it. The search engines understand this and will give you some leeway as a result. Nevertheless, it's in your best interest to investigate the sites you are considering linking to wherever possible, and make an informed decision about whether you want to link to them, and how you want to link to them.
1st impressions are often the best guide when you visit a new site. Does the site instill you with confidence? Does it look like the webmaster takes their site badly, or are they just slapping up any old content, and spamming the site with keywords? Are there obvious issues with spelling and grammar, and with page layout and site navigation? Does it make you want to stay, or leave?
Is the content on the web site related to your site, and in particular, is the page that you are linking to relevant to the page that you are linking it from?
You may also wish to check out some of the sites that the linked site is itself linking to. Are these quality sites and are they relevant to the page they are linked from? And yes, I know what you're thinking - "Where does it end?". A quick and cursory sampling of a small, random selection of the linked sites is all that you need, but this can sometimes tell you more than all the other factors combined. Remember that search engine link juice can flow a long way along the link chain.If your overall impression of the site's quality and relevance is good, then you should consider do-following it. If it is bad, or you don't have the opportunity to check the site out, then consider no-following it.