Every week I shoot pictures of speakers at a club meeting. The conditions are terrible, there's usually something on the wall or a table behind the person, and I often can't use bounce flash because of the position or distance, so I end up with worse shadows than this. My photos are just going into a pdf newsletter on our web site, but I still like them to look as good as possible.
The way I get rid of this type of shadow (using Photoshop Elements) is to select the subject (person), refine the selection as needed, then invert the selection. Then I use the Clone Stamp tool to clone in a well-lit part of the background into the shadow area. By doing the selection first I don't have to struggle with keeping what I'm cloning from spilling over onto the subject.
This also works well to get rid of coffee pots, fire extinguishers, thermostats, etc.! 