i would agree that there are no ways to know who visited your page. Please do not fall for those links that promise to let you know who visited your profile when you visit them. If you do not have a proper internet security, this could bring you to serious trouble as this links usually messes up with your computer either by planting a worm or a virus. I bet facebook did not really opt for that functionality so we just have to deal with that.
No way for facebook mate. In case there is an app claiming it can do it, it's one of the many malware floating around facebook. So i guess you need to be a little careful next time some app says it can do that.