I had an idea for a Facebook app the other day. I wondered who actually looked at my profile and thought I could create a Facebook app that would record this information and display it. When I talked to Vishu though he said that this wasn't something that Facebook would be too happy with. Indeed the Platform Policy explicitly disallows this in section 2.8. This explained why the app didn't already exist. Its probably for the best since everyone assumes they can anonymously view Facebook profiles and would be irritated if that weren't the case.
On the topic of assumed anonymity, check out this article on the aggregation and selling off of your cell phone data including your physical location.