When you first start learning photography, you learn that shadows are bad. Many sources condemn shadows, claiming that they are distracting or intrude on the face. Now I'm not criticizing the instructors or books. They are right. The wrong kind of lighting can produce unflattering shadows. Think of the overhead lighting from bright mid-day sun. It cast shadows under the eyes, nose, and chin in such a way that is never flattering to a subject.
But, like a lot of things, it's easy to take the idea of reducing shadows to an extreme. Instead of working with the lighting to create flattering shadows, the latest trend seems to be a shadowless image. The problem with this is that the image becomes very flat and two-dimensional.
If you look at classical art styles, you see that they use shadows to show dimension in their work. The shadow and highlights in images give a two dimensional art form a three dimensional look. The art "pops," if you will.
There is a reason that a lighting technique in photography is called Rembrandt lighting. It was derived from the artist Rembrandt's paintings. If you study his work, you see a triangle of light on the shadow side of the face.
If you take your subject's face into consideration, you will find that each face shape benefits from different kinds of lighting. You can use the shadows in your favor to thin a round face. Conversely, you can widen a narrow face by reducing the amount of shadow.
Additionally, shadows can enhance a composition. Shadows exist in life so why would we erase a shadow from an image? For example, if your model is close to the wall, why flat light them? If you play with the angle of your lighting, you can produce a flattering shadow, not a halo shadow you'd get from an on camera flash, but a natural shadow that could appear in low afternoon light. By adding this kind of flattering light, you've created interest, time, and an additional compositional element in your image.
Play with your lighting. Some setups will fail, while others will speak to you. But if you never experiment and fail, you will never learn when a shadow is good and when it is unflattering. It takes a little more work to set up your lights to produce shadows in the right places. It also takes patience and direction from you to your model so they know exactly where to pose causing the light hits them correctly. It's easy to throw a lot of diffused soft light on someone and shoot a series of very flat lit images, but if you take some time, create directional light, and pose and setup your image, you can create more memorable images with different looks and shadows. Think of it as painting with light. You don't throw a bucket of paint at a canvas and call it art. You meticulously add the dabs of color where you want it in order to create the artwork. Well, try meticulously adding dabs of light to your model and see the difference it makes in your images.