Facebook has over 1.2 billion accounts, and even if you sat at your computer all day for the next decade, there is no way you're ever going to be able to visit every one.
The next best thing, though, is checking out everyone's profile picture on a single page, which is exactly what freelance designer Natalia Rojas did when she created the Faces of Facebook website. At first, the website looks like the static of a television screen, but once you zoom in, you'll see a sea of strangers' faces, all taken from their Facebook profiles. While it might seem disorganized and nuts, the page is organized by the order the users registered. If you haven't changed the Facebook user name, that number might be in the URL of your profile page (if we remember correctly.)
At least for us, the site seems to be getting a lot of traffic right now, and is taking a little long to load. But, give it a try here, and let us know if you're able to find yourself. We're not expecting many responses.