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: 
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.
My policy, that has served me well, is that I never, under any circumstance, add coworkers to my Facebook "Friends List" until I have left the job.

I can't see any good coming out of adding anyone while we are still coworkers. I don't need anyone monitoring my every move and I don't like having to think too hard about who is in what group when I am sharing opinions and personal thoughts. 

What if I decide to post that I'm heading to an interview (which I do occasionally just to test the waters) or if another friend asks me about a recent interview experienc? 

Can everyone I work with be trusted with that info? Even if one person can be trusted, they are like a vector by which another (untrustworthy/gossipping) employee could gain access to information I provide. 

What happens when a nosy or hostile coworker steals a glance at their phone FB wall while they are distracted etc.

No coworkers...ever...this works for me since I tend to change jobs every 2-3 years anyhow. While I'm at a job, if we really are friends, then we probably don't communicate primarily through FB. If we are friends, we will have each others phone numbers and can text/call/im/email to arrange pretty much anything.