Well, of course I am writing this since I am sick with an infection caused by allergies. First, light aerobic exercise is fairly safe as long as you are not running a fever.
Avoid heavy weightlifting, this causes a decrease in the Killer T cells in the blood for a few hours after the workout. These cells help fight infection and sickness.
Experts like to cite a rule of thumb known as the "neck rule." If your symptoms are all located above your neck (stuffy nose, scratchy throat, headache), you almost certainly have a head cold and can hit the road or treadmill safely. If, on the other hand, you have a fever, congestion in your chest and lungs, or feel achy, it is probably a sign of flu, bronchitis, or another more serious ailment, and you should rest up.