Do you have a Facebook page for your library?  If so, these 2 ideas tweeted by Kimberly Brosan look like good ideas to try:

• "For Random Acts of Kindness week, will waive overdue fines of students who become a fan of library on Facebook" [http://twitter.com/KimberlyBrosan/status/37134687717695488]
• "just reduced max fines to $1 for HS students. Going to ask them to like us on FB and I'll waive fines. Hope it works!" [http://twitter.com/KimberlyBrosan/status/35703458610946048]

What methods have you tried to encourage people to "friend" your library's Facebook page?  Please share them in the comments so others may benefit from your ideas.  :-)