There are quite a few scams involving Facebook, so you should always keep an eye open on fishy situations; however, sometimes you just lower your attention a bit and you don't find out right away that you've been involved in a scam.
Two of the most recent scams I've heard of (or I've been witnessing) are:
- the new (fake) account of one of your friends;
- the desperate request for help (and money) from a friend.
In the first case, you receive a friend request from one of your friends... only, it's not your "real" friend but it's someone using their picture and name, trying to access to all sort of info about your life (according to what level of privacy you are using with your friends).
It looks like a stupid scam (why the heck would someone send you another friend request!) but sometimes you just got distracted and you don't realize this person is already on your friends' list. So please, before accepting a friend request from someone that you know, please take a moment to check if you are already “Facebook friends” and, if you are, give this person a call and recommend to warn friends and family about what's going on.
The second scam is pretty creepy: someone knows that one of you friends is away for a holiday and send you, under a fake profile, a desperate request for help and money because something terrible had happened. Avoid to panic and do your research to see if this request is legitimate – usually it's not.
A last advice: change your Facebook password frequently. Someone suggests once a month, maybe it's a little drastic but please do it from time to time. Use a combination of letters and numbers that are directly related to you (like your date of birth) and change it periodically.