When you're sick, your body is telling you it needs rest, although a short lighter workout is often good to keep the blood flowing. Doing too much can put a strain on your kidneys and other organs, and can lead to complications or just drag the minor ailment out alot longer-- and no one wants that!
If you have a fever, PLEASE stay out of the gym so you don't infect those of us who don't!
I never run or do alot of aerobics with a cold, but will do some easy biking, pilates, and yoga or other stretching.
But as others have said-- it's all about how you feel and how fast your body heals.