I'd love a feature to appear offline or "invis" as my status. I love my friends but sometimes I just want to be left alone and setting myself to "busy" just doesn't cut it. Sometimes they go as far as to check my in game location and hunt me down, so I have to just stop everything and let my character go afk so that they'll leave me alone. :/
I hate just ignoring them and then having to listen to them complain that I did so.