The ball must not strike the flagstick 

(A) If it is attended or being held up, even if the stroke is being made from off the green.

(B) If it has been removed from the hole,

(with the players authority or prior knowledge by someone in the players group)

 Again, this applies even if the ball is played from off the green.

 (C) If the player is playing a stroke from the putting green.

The rule that covers this is R17-3, the purpose of the rule is to prevent a player using the flagstick as a backstop or in some other way to aid his play. The penalty for hitting the flagstick in any of the above circumstances is loss of hole in match play or two strokes in stroke play. A player may have the flagstick attended or held up at any time but if it is, then it is deemed to be attended until the ball comes to rest. Apart from hitting the flagstick the ball must not strike the person attending it or holding it up. It is worth noting that the flagstick is considered to be attended if someone is standing close to it, even if they are not actually touching it.

So what if the a player sees that the ball is likely to strike a flagstick that has been removed from the hole? As from the 1st January 2008 it is permissible to lift it so as to prevent a ball striking it.

Sometimes the ball is so close to the hole that the player will remove the flagstick  holding it in one hand while putting out with the other. Then the cry goes out;- Penalty! There is nothing in the rules that forbids this and it is quite acceptable to do so, providing of course, that the ball does not strike it.