Before I answer your question, Morecy, I'll expand a bit on what exactly the dimple principle is. Settle in.
Basically, there are three primary types of drag acting on an aircraft: induced drag, skin friction drag, and pressure drag. It is pressure drag that is the main factor involved in the dimple design's existence. Pressure drag is primarily the result of a moving body's wake. Depending on how soon the airflow separates as it passes over an object - that is, how far along the object the flow travels before no longer following the contour of the object - the size of the wake will be larger or smaller. A larger wake equates to more pressure drag (put simply, there is a larger region of stagnant air behind the body meaning the airflow pushing on the front of the body has less impeding its production of drag) and vice versa.
Now, imagine a sphere. Because its height/diameter is large in comparison with its length, it is what's known as a "bluff body." Bluff bodies such as a sphere have disproportionately large wakes, and as a result they have disproportionately high pressure drag. (This is compared to both their own skin friction drag and a not-bluff solid's pressure drag). Obviously, then, overall drag on a sphere (or other bluff body) can be dramatically reduced if pressure drag is reduced. That is, pressure drag is what you want to specifically target and minimize.
Enter dimples. Dimples turbulate the airflow over an object, thus increasing the flow's kinetic energy. This acts to delay flow separation, which then leads to a smaller wake, which in turn leads to less pressure drag. And this solves the bluff body problem! Because bluff bodies have such high pressure drag compared to their skin friction drag, what little extra of the latter drag is created by dimples is more than offset by the drastic reduction of the former drag. So a golf ball - the classic example of a bluff body - will travel farther with dimples than without, and that is of course why they have come to carry these dimples.
Now, to finally answer your question: 'normal' aircraft are very simply not bluff bodies. Dimples would create more skin friction drag than they would reduce pressure drag, defeating their purpose.
I've probably told you more than you needed to know, but hopefully that was at least fairly understandable, and not too boring!