I guess the first thing to consider in this question is a definition of popularity. In some circles that word means that others like you. But in the blogosphere that term appears to mean that others visit you, comment to you, recommend you via links and trackbacks, and add you to their permanent rotation via a blogroll, a bookmark, or favorites list.
So should a blog worry about achieving such recognition, should it in other words try to be popular? Some blogs start right out asking you to recommend them to others. Buttons appear, usually at the bottom of a post that allow you to favorite them by saving to del.icio.us or technorati or to Stumble It! or to Digg This! There are dozens of these services. All available to link you to friends and popularize them, too. But does this mean that because everyone else is doing it, that you should to? Or should you wait and let them come to you.
Screen views are another way to increase your popularity quotient. The more the merrier appears to be the way. Screen views can be measured by duration (how long you visit) or by frequency (how often you visit). This seems relevant either way but who’s to say whether frequency beats duration except is sex where they are both neck and neck. One of the easiest ways to get started here is by setting up a companion site at one of the social networks, www.myspace.com or www.youtube.com.
Meanwhile, two other ways to reach an audience of fans is to allow the visitor to subscribe to a rss reader or an email delivery service. www.feedblitz.com and www.feedreader.com will both set your blog up with buttons to click. My favorite of course is the one that carries my blogs. Still, have we really answered the question?
In real life, the harder you work at being popular the harder it may be to become so. The same may be true of blogs. My take is to keep your blog real. Make it have your voice. And then see what happens.