That's why HDR Processing was created. Because often one exposure setting will only do part of the image justice, and the rest will be under, or over, exposed. With an HDR processor you can take three pictures, and the program will mold them together so that every part of the image is exposed just right.
Do you really think this winning image that landed the cover of "Outdoor Photographer" magazine could have been made with out HDR?
No. Come on, think about it. You point your camera at the flowers, the sky would be way washed out. Point it at the sky, the flowers will be wreathed in shadows, they just won't have that glow.
How about an example of my own?
Photomatix Pro is reputed to be the best HDR software out there. You can download the free version easily, but the full version costs $99.
The free version can do everything the full version can, except it will leave a "Photomatix" watermark on your photo.
Example:
Combining the three pictures above in the Photomatix Pro, I came upwith the following image:
Here we have an obviously superior image, but it is unusable without payment do to the watermarks.
There are several free-ware HDR programs out there too, including Picturenaut and Luminance. I haven't found these to be as good, but I'll post again if and when I decide that they are indeed a stable alternative to Photomatix.