The truth about those weird Facebook friend requests 

Question: A few of my Facebook friends sent me messages saying they got a Facebook friend request from me when we're already friends, and that I may want to check my account and forward the message to others. What should I do?
 
Answer: It's entirely possible that your friends did get a bogus friend request from someone who created a fake account with your name and photo. It's easy enough to find out; simply do a search for your name on Facebook and see if another account with your name and photo pops up. If that's the case, then, yes, you should inform your Facebook friends that there is a duplicate account that may be trying to friend your friends.

You should also click on the Report This Profile button on the fake profile to report it to Facebook, which should shut the account down within 24 hours. A duplicate account isn't necessarily harmful to you, but the person who created it may be trying to get others to friend them so they can mine those accounts for personal information.
 
Another possible scenario is that your friends simply forwarded a message they got from another friend saying, "I got a bogus friend request from you. Forward this to everyone you know." Before you go spamming all your friends, you might want to message these friends back and ask if they really got a duplicate friend request from you, or if they just forwarded the message because they were asked to.