Question: I consider Facebook to have information that is personal and that I only share with close friends and family. However, in my new workplace I’ve been asked several times for my Facebook username and/or have been *friend requested* and I don’t want to sound rude by telling them that I don't want to add them as friends. 

Any suggestions on the way I should handle this?

Answer: 
Tell them that you keep work relationships out of Facebook as a personal policy (and suggest they connect with you on LinkedIn instead, if you use that for your professional network).
My policy, when I was on Facebook, was very simple: Friends were just that, *friends*. I didn't add acquaintances, I didn't add every coworker, I didn't add folks whom I knew by sight but hadn't spent a significant amount of social time with. Period.

You don't have to respond to the request. Just ignore it, and let them deal with it. But you also don't have to feel bad about saying "Thanks, but no; I'm keeping work and personal life separate."

Ditto for any other social medium, unless you're in a situation where you're trying to do business via same... and then I'd suggest a separate account.