Are you talking about adding a site to your "favorites" or a social bookmark like Digg?
If favorites, no. However, if a user adds to favorites and visits your site often, there is a good chance that they told friends about it, possibly increasing your Alexa rating (which isn't a big factor) and they may like your article/site, tweet about it or add it to social bookmarking sites which in turn will give you nofollow backlinks in the future.
If you're referring to social bookmarks, it is a backlink, though doesn't pass link juice onto you. You may see a a lot of visitors all at once and it die down to zero or a steady amount of visitors from (popular) bookmarking sites.