Obviously the more people who view your site the better. And there's an indirect benefit in that it will significantly increase the likelihood that bloggers will link to it voluntarily. This offline linkbait can be very powerful.
Take the case of the nomadic Aussie comedian Jimbo. He has a very unusual companion: a goat called Gary. This friendly herbivore, who sports a colourful cap, always turns heads wherever he goes. He also gets into a bit of strife occasionally.
One time he ate some flowers outside Sydney's Museum of Contemporary Art. This faux pas put his owner Jimbo into a spot of legal bother, although the case was eventually thrown out of court.
In any case Gary and his owner became very widely known as a result of this and other escapades. So now all Jimbo has to do to get social media buzzing, and some mainstream media attention, is to take Gary for a walk through the CBD. All that social activity is a boon to Jimbo's site in several ways of course. And the odd dofollow link results from online news reports such as this one.
This phenomenon is well worth noting if you are a webmaster or blogger. If you can manage to do something consistently eye-catching and perhaps a bit eccentric while remaining true to yourself, there's a good chance you can use it to benefit the URL's standing on social media and the search engines.