I started my blog (musicsnob.wordpress.com), and then a couple weeks later upgraded to having my own domain (oxfordmusicsnob.com). Now, when I view the pages of my blog, it does not appear that I'm logged in. I can also tell that my views of my pages are counting in the statistics (due to the not logged in issue). When I want to reply to a comment on a post, I can tell I'm not logged in. The main evidence is that I don't have the blue nav bar at the top when I browse my site.
Note...I can log in a view my admin area, but then when I view any of my pages, it logs me out.