It is not uncommon to find articles dealing with strength training for runners. What is surprising, is that many of them advocate strengthening only the upper body since, in the authors opinions, the lower body is already sufficiently strong from the running. This, however, is a fallacy.
In the early stages of running, there is some strengthening of the muscles in adaptation to increased running speeds. However, once you develop yourself to the point where you run at a regular pace, there is no further strengthening. There is, however, improvement in the cardiovascular system so that in time an imbalance develops between your strength levels and your cardiovascular and respiratory system development.
Because of the improved circulatory system functioning, you feel less stress in the running and, as a result, believe that you can go further and faster. When you make a significant change, because of the minimal strength in the legs, you invariably come down with an overuse injury.
Thus, it is important that you also strengthen the legs to enable you to go faster and further in coordination with your aerobic capabilities. Most effective are strength exercises that duplicate exactly what occurs in running, i.e., you strengthen the muscles and joint actions as they are used in running. In this way, you strengthen the muscles which have a direct effect on your running speed and distance and at the same time, help to prevent injury.
In addition to greater strength in the legs, you should also develop the muscles around the midsection to hold you in an erect position during the run, prevent excessive rotation of the shoulders and at the same time allow for full range of movement of the pelvic girdle to give you full stride length and speed in your run.
Upper body strength is important mainly to balance your muscular development throughout the whole body so that you are harmoniously developed. By doing some exercises that duplicate the arm action in running you may also enhance your running abilities.
For more information on strength exercises that are specific to running, and how you can improve your running technique, see Explosive Running.