Great idea! I always forget…Thanks!
How to remember all my loved ones' birthdays
It made me
Relieved. 
"Friend everyone on Facebook, and let it do the heavy lifting."
How I did it: Corralling birthdays is like herding cats. I'd get them in my address book, then forget to look; I'd put some in my calendar and never have the address or email handy to send a greeting.
Facebook is terrific for this. I check in once daily, in the morning, and either post my regards in the stream or send a private email (NOT via the Facebook system).
It's a lovely, simple way to stay in touch at least once annually, and tends to prompt more connection the rest of the year.
Lessons & tips: If you have a to-do list of some kind, put "check Facebook for birthdays" every day until it's an automatic action. I've been doing it for about a month now; I hear it takes 60-ish days to turn something into a habit, but YMMV.
Resources: Uh...Facebook!
