I have found that strength training is the best way, other than actual running to increase speed. Working every day, or every other day on a pre planned route, a mile, two miles, whatever the distance your trying to improve speed on is one and maybe the most popular way to increase speed. You will increase stamina which in result will give you the ability to run faster longer.
However the other way to gain speed is through leg and other body part strength training.
For Example:
Knee Drive-This exercise duplicates the action of driving the thigh forward, which is important for increasing speed and stride length. Using rubber tubing, attach one end to a stationary object about knee high behind you and the other end to your ankle. Stand far enough away so there is tension in the tubing when the leg is behind your body. Hold on to a partner or something stable for balance. Your thigh should be free to move through a full range of motion. Stand erect with the exercising leg behind the body as far as possible to duplicate the thigh position immediately after pushoff. When ready, drive the thigh forward with your knee bent and shin basically parallel to the ground, until it passes the vertical position. To duplicate more closely what occurs in running during the knee-drive phase, keep your trunk erect, fully straighten the support leg, and rise up on the ball of your foot as you drive the knee forward. Once you're comfortable with the exercise, perform it at a moderate rate of speed to develop greater strength. Warning-don't press the thigh upward to a parallel position with the ground. In the running stride, once the leg passes the position slightly in front of the body, the thigh continues on momentum to reach its uppermost thigh position.
Pawback-This exercise duplicates the thigh pawback action-the down-and-back pulling action of the leg to make contact with ground. Using rubber tubing, attach one end to a high stationary object in front of your body and the other end around your ankle. Stand so that when the leg is raised, with the thigh slightly below parallel, the tubing is vertical. When you are ready, straighten the leg and pull down and back fairly vigorously. Initial ground contact should be with the whole foot or the ball of the foot. Inhale and hold your breath as you pull down and back, and exhale and relax as you bring the leg back up in preparation for the next repetition. Balance your body in an erect stable position during execution. Hold on to a partner or something stable for balance.
So as I said, if your not looking to increase speed by increasing stamina, then these are two VERY good exercises that will help in increasing running speed.