It goes without saying that keeping your brakes in good working order is a must. Check your brakes often to make sure they are contacting the rim and not the tire. If your brake pad is rubbing the tire, you'll have a flat on your hands very soon. Also, make sure your brakes are centered over the front and rear wheels by spinning the wheels while you lift the bike off the ground. If your brakes are off center, your rim could rub the brake pads and slow you down. If the brakes appear off center, first pull off the wheel and re-center the wheel to make sure the wheel is in correctly.
Brake is contacting rim:
Centering the brake on the rim:
Brake not dragging on rim: