It is not possible for a Facebook user to see the profile of another user he or she is not friends with, unless the profile is made public by the other user. Applications that seek to circumvent these privacy controls have not been made available.
Facebook gives users a great deal of control on who sees their profiles and what information is public, visible to friends only or visible to certain friends only. A user can fill out his or her profile with as much information as he or she would like, and set the privacy settings for each post or photo he or she puts up. A user may also create lists of friends, which allows posts to be shared with only a certain group of people. There is also a "View As..." option in Facebook's privacy settings that allows users to see what their profile looks like to the public.
However, attempts to get around these privacy controls have been made by application developers. Stalkbook is an app that uses another user's credentials to allow someone else to see a person's profile. However, because this violates Facebook's terms of service, Stalkbook has not been, and most likely will not be, made available to users.