Photographers use HDR in many situations. When shooting outdoors at sunrise and sunset, this technique produces remarkably beautiful images. If overdone, it can look surreal, but if used with a gentle hand, it can look stunning.
When shooting during the middle of the day, HDR is the only technique that can deal with the unattractive contrast associated with direct sunlight. Digital sensors just can't reproduce what we can see with our eyes, and by shooting several exposures and then combining them into one composite we can reveal detail in the highlights and shadows that would otherwise be impossible to see. In the photo above, for example, without HDR the sky would either be blown out (solid white) or the shadows would be black. If you don't use HDR regularly, it's time to start because it addresses the biggest problem in photography.
In this picture of Stonehenge in England, notice the wonderful detail in the shadows as well in the very bright sky. Had I not used HDR, this picture would have been terrible.