Golf ball has dimples on its surface because we want a turbulent boundary layer. Golf ball is a bluff body (i.e. the drag is dominated by pressure drag). Hence, the drag on a sphere is dominated by the separation on the rear face. If we could minimize that, the drag would be reduced.
The following figure shows the variation of drag coeffecient of a sphere with Reynolds number.
Image from wfis.uni.lodz.pl, taken from (Hoerner 1965)
As can be seen, the drag reduces at the critical Reynolds number, which is the point where separation takes place. Because of separation, the wake in the rear of the sphere (or ball) is reduced, which reduces drag. So, if the boundary layer of a sphere can be made turbulent at a lower Reynolds number (by some means), then the drag should also go down at that Reynolds number, as a result of the reduced wake. This can be seen in the following picture, where the flow has been made turbulent using a trip wire.
Flow over a sphere: (a) Reynolds number = 15,000; (b) Reynolds number = 30,000, with trip wire. Image from princeton.edu
That is the purpose of having dimples in a golf ball- to reduce drag by inducing turbulence and delaying separation (this can be achieved by increasing the Reynolds number; but we are limited by the ball speed). The resulting wake is much smaller due to the delayed separation.
In case of a streamlined shape (like aircraft wing), the propotion of pressure drag is small, as can be seen below.
Image from pilotfriend.com
In case of streamlined shapes, the pressure drag is small because the wake is small. The net result is that 'tripping' the boundary layer as in bluff bodies is not a good idea (a laminar flow causes less friction drag than a turbulent one).
The aircrafts do use similiar devices, via the vortex generatorvortex generator, which are used mainly to delay flow separation.
