Can Someone Find Out How Many Times You View a Facebook Page?
If you get a Facebook message from a source that claims its application knows who views your profile and you can download it from a provided link, the message is a scam -- and likely forwarded without the message sender's knowledge. Facebook does not provide applications to profile owners that identify who views their profile, even through third parties. You yourself cannot be tracked unless you are infected with malware or you submit to being tracked. So don't be afraid of "stalking" a page; no one will find out.
Tracking on Facebook
By default, all the information any third-party application has about you is limited to public knowledge -- what you allow anyone to see. However, many applications ask you for access to otherwise private information. If you opt in, you may be tracked. Facebook does not sell information about your activities to other users.
Limitations on Tracking
Facebook does not have the ability to track who views a particular person's profile. Nor can any other program provide this functionality; doing so is against Facebook's Terms of Service. However, some applications can track a user's actions, including knowing if they visit a particular website or profile. An application needs specific permission in order to track your actions. Denying that permission prevents it from tracking you.
Never install an application with a single click from another user's profile; this is how most scams are spread. Virulent apps track your actions and post messages pretending to be you to your Facebook Wall, encouraging others to follow in your steps. Do not allow these programs access to your Facebook Account. If you believe that your friend is recommending an illegal app, message them back and ask if they meant to post that message. This confirms the legitimacy of the app and lets them know if their account has been compromised.
You may have noticed that some app websites claim to be able to let you know who visits your profile; this is a false claim. These sites often contain malicious software; they draw clicks by promising to offer a service that no one else can do, but most are viruses or other scams. Installing them may compromise your personal information and then post messages to your friends with the same claim. Facebook recommends that you report any applications that make these claims so they can be removed.