Do all A320-family planes have leading edge high lift devices?
Unless something broke mid-flight -- which you would have probably been told about as a passenger because of the faster landing speed -- leading edge devices (slats) are used for takeoff, approach, and landing on the A320-family.

For takeoff the slats are put in position 18 or 22, and for landing in position 22 or 27, as the table below from an A320-family flight crew operating manual shows:



If you are sitting well ahead of the wing, you may not notice a change if you don't know what to look for. Here are the 4 positions:


(YouTube) Slats 0, 18, 22, and 27. Also note the arrow showing the 3 extended position markers.

One of the few jetliners built without slats is the DC-9 Series 10.


  The Series 10 was unique in the DC-9 family in not having leading edge slats. The Series 10 was designed to have short takeoff and landing distances without the use of leading edge high-lift devices. Therefore, the wing design of the Series 10 featured airfoils with extremely high maximum lift capability in order to obtain the low stalling speeds necessary for short field performance.


The rationale would have been weight and maintenance cost saving, which was helped by the short range of the plane. For faster cruise speeds and longer range, high-speed tailored wings with slats for low-speed are better than low-speed tailored wings.