Assess your symptoms. If your troubles are above the neck, moderate exercise is probably OK. For example, if you have a cold and no fever, a walk may be fine.
If you have flu-like symptoms and a fever, rest.
Do not work out hard for at least a couple of weeks if you're really sick. Your body needs to concentrate on healing.
Start slowly when you return to exercising. You will have lost some strength, but it will come back faster with patience. Don't beat yourself up and get sick again.
Sleep, sleep, sleep. Your body needs the rest time to repair the immune system. Also, if you are stepping up the exercise intensity quite a bit, you may even need more sleep. Try for at least 8 hours per night.
My one teacher's wife died of an anurism (sp?) because she jogged every morning (addicted to it) and didn't want to miss a day. She had the flu.
Left him and their baby daughter behind. So I say, give your body a chance to recoup and then go gymming again. If you think that you will leave loved ones behind just because you didn't want to miss your next "runners high"
If you have a Flu, never go to the gym. Even though you think there is no damage being done. Massive damage is done to the heart. If it doesn't effect you there and then.... It will affect you later in life.
It's just good advice, obviously it differs from person to person. But again I say this: It's not worth the risk