What I did was create a friend list called "close friends" that excluded the problem person I knew, and when I post something on my wall, I set it so that only people on the close friends list can see it. This can be alternative to the "drama" of unfriending someone.
I had to do this because one woman I knew would be all over my facebook page all day long, commenting on every single picture I posted in my albums and talking on my wall, often rambling on and on, for no reason. Also, she met a few of my relatives one time at a party at my house, and then she sent them all friend requests, they accepted for whatever reason, and now she pesters them constantly on their facebook pages too. I am pretty sure one day they'll either unfriend or block her.