As an orthopedic physical therapist who builds custom orthotics and provides custom orthotic therapy, one might be surprised that I am also an advocate of barefoot running.
I believe that running around barefoot forces the foot into an ideal posture for running unlike the sophisticated running shoes on the market today that allow and even encourage running.
The runner who is a “heavy striker” is a great candidate for barefoot running. While there have not been many studies examining the benefits of barefoot running compared to shod running, the fact is that there is a lower incidence of chronic injuries associated with barefoot running. In fact, an article in Sports Science notes that “running barefoot is associated with a substantially lower prevalence of acute injuries of the ankle and chronic injuries of the lower leg in developing countries”.
The heel strike is a normal part of the normal gait cycle in walking, but in running, it is preferable to be a mid-foot striker rather than a rear foot striker. Heel strikers are “puling themselves along” while mid foot and fore foot strikers are “pushing themselves along”. I encourage heavy plodders to try to run on their toes in order to move the strike toward the forefoot. In contrast, look at this image and see both the body posture of the runner and how by leaning forward his strike is naturally more underneath him, and as such, is naturally more of a forefoot or even mid foot strike. 
I have found that one of the best ways to do this is to run barefoot. By running barefoot, there is a tendency to stay off the heel because excessive heel strike is actually painful, which should tell us something about the way the foot is designed. Remember, there is good evidence from at least a couple of world class runners, that barefoot running does not interfere with performance and, it may be argued, that barefoot running might even enhance performance.
I also want to promote a great new shoe to assist one in their barefoot running efforts. The Vibram Five Finger Classic Water Shoe, shown below is a really useful way to get into barefoot running so that as one does so the risk of injury to the sole of the foot is minimized.

Vibram Five Finger Classic Water Shoe
The shoe is available at REI for example, and costs about $75.00. Pretty good value. The people I know who are wearing the shoe are very impressed with the feeling they have about the shoe and how it gets them onto their toes during their runs.
So the take away is this: If you are having trouble as a runner with chronic injuries, or if you are a really heavy striker and you can hear your self running, or if you describe yourself as a really “heavy” runner, then you might be a really good candidate for barefoot running to help you re-educate yourself to be more of a forefoot or even a mid-foot striker. If you go in this direction, then the Vibram Five Finger Classic Water Shoe might be a good solution for you.