RULE: Ahh - my ball has moved by iteself!

Answer: You play the ball as it lies.  You do not replace it or incur any penalty.

Rule 18, “Ball at Rest Moved”, covers cases where the ball is moved.  For a full description, see the Rules of Golf but the following are the main points.

If the ball is moved by an outside agency, then the ball is replaced without penalty.  Note that wind and water are not outside agencies.  Ducks are!  Well, what is an outside agency? See definition p. 39 of the Rules of Golf.

If the ball is moved by the player, his/her caddie or equipment, then the ball must be replaced and the player incurs a 1 stroke penalty. 

The exception to having to replace the ball is if the ball moves after the player has begun the stroke or the backward movement of the club for the stroke and the stroke is made.  There is still a 1 stroke penalty.

If in stroke play the ball  is moved by a fellow competitor, his/her caddie or equipment, the ball is replaced and there is no penalty.

If the ball in play and at rest is moved by another ball in motion after a stroke, then the moved ball is replaced without penalty.

But, what if ...... ? See p. 82 of the Rules of Golf for the circumstances when there is no penalty if a player accidentally causes the ball to move.