I have gone through all my privacy settings going "just me", but now I find that when real friends (who are not already Friends on Facebook) find me, they cant ask me to be their friend - because there is no button!
Under Privacy Settings, click on 'Edit Settings' next to How You Connect. It will give you choices for: Who can look up your profile by name or contact info? Who can send you friend requests? Who can send you Facebook messages? Who can post on your Wall? and Who can see Wall posts by others on your profile? (Note: Stories about likes, friendships, and some other types of wall content aren't included in these settings.)
Uses the drop down menu to the right of each of the above to select who can do what.