It is all to do with tripping the boundary layer to make it turbulent sooner (i.e. moving the transition point forward). Turbulent air has more energy, so will stick to the surface further around the back-side of the golf ball. This decreases the profile drag a large amount, but for a small increase in skin friction drag created by the dimples.
Aircraft wings do not need dimples because they are not golf ball shaped. However, at strategic places, like in-front of flaps or ailerons, where there is a danger of flow separation, this movement of the transition point forward is done with vortex generators (as gas bags stated). It has exactly the same effect.
(Sure, dimples would do the same thing, but the fact that an aircraft wing is far more predictable re its orientation through the air than a golf ball is, the designers can be far more discerning when it comes to placing the flow-trip devices)
Great description of the golf-ball effect and how it is applied to aircraft is here:
Aerospaceweb.org | Ask Us - Golf Ball Dimples & Drag
Hope that helps
Doppleganger
Aerodynamics Lecturer