While en route to his destination, the 12,250-hour airline transport pilot experienced variations in the airplane's cabin pressure. The pilot removed his noise-cancelling headset and was able to detect an air leak from the area of the entrance door. Moments later, the airplane encountered turbulence and the door departed the airplane causing substantial damage to the fuselage. The pilot declared an emergency and was able to land at the nearest suitable airfield. During his preflight inspection, the pilot, who reported 5,200 hours in make and model, secured the door "normally," but could not recall if he visually confirmed that the door was secured. The fuselage door frame did not display signs of deformation where the entrance door's bayonets seat into the door frame. The door was not recovered and an examination for mechanical failure could not be conducted.