If you use Facebook, there's a good chance you've encountered some app or some friend claiming they've found a way for you to see who has been viewing your profile. Chances are, it was a scam.
In fact, a few months ago, there were reports circulating about such scams. One in particular, security firm Sophos said attracted 60,000 clicks in just a few hours. Such scams still pop up from time to time. Your best bet is to ignore them, no matter how curious you are.
Facebook has acknowledged in the past that there is no way to view this information, but a post on Quora makes it pretty clear that there never will be a way either.
When someone asked the question: "Will Facebook ever offer a feature like LinkedIn's, where you can see who has viewed your profile, Facebook Director of Engineering Andrew 'Boz' Bosworth simply says:
From the sound of it, you probably have a better chance of seeing a Facebook-branded phone.
My advice to you is to only let people you want to see your profile be your friend on Facebook.