Translation:Please don't smoke anymore!
Good point, but there's a subtlety here. You can say this Chinese sentence to either
(a) A person who is smoking right now, or
(b) A habitual smoker, who may not be smoking at the moment.
In case a), you are basically asking the person to stop smoking. 再 = any longer (or maybe "anymore" as well?)
In case b), 再 = (ever) again. To be unambiguous, you could start the sentence with 以后 (in the future), or use 再也不要 instead of 别再.