People You Don't Know at All
Complete strangers should never be on your friend list. If you get a friend request from someone you don't know and there isn't a message explaining who they are, hit "ignore." Facebook will then ask you if you know this person outside of Facebook, and you should say "no." That way, they won't have a chance to friend you again.
If there is a good reason why a complete stranger is sending you a friend request (such as, you're mildly famous or have a job where you regularly interact with strangers on the Web), then you might consider it. Otherwise, just hit ignore, because these people will never really be your real friend.
Don't Send Friend Requests to Your Ex's
If you weren't friends with your ex before your relationship, it's probably not a good idea to try and be Facebook friends now. Facebook should be an extension of your personal life, which means developing your relationships, sharing pictures, and having more communication with genuine friends (real life or online). However, if you friend someone based on the fact that you used to go out and then broke up, you're beginning things on a negative note right from the start.
It might be tempting to see what your ex is up to, but you'll probably get more information that you ever wanted or needed. Look at their friendship as the equivalent of going back a few steps into the past. Do you really want to do that?
Wait Before Friending Acquaintances
Never Friend Your Bosses, Coworkers, or Clients
It's one thing to encourage a work friendship, and other entirely to show them your life in a public way, as you would if they were on Facebook. You should try to get on friendly terms with your coworkers if you can to help with overall job satisfaction and work environment, but be cautious before sending that Facebook friend request. If your coworker hasn't been to your house for dinner a few times, I wouldn't consider friending them on Facebook. Bosses and employees should never be friends on Facebook.
If you talk frequently with clients, they too might want to hang out with you in the Facebook world. But unless you're comfortable with them seeing pictures of your kids and special family moments, I'd tell them you only have a few close friends in your Facebook list. You could even tell them you don't use the site that much. That should satisfy any complaints about denying their request.