Completely dependant on the type of exercise and the type of sickness. I've had colds before where I kept training just the same. I find that being active helps to open me up when I'm sick, and the increased circulation makes me feel much better. This is especially true oh headaches. Nothing helps a headache like a good training session.
That being said, I wouldn't feel bad if I had to miss a session or two because of health issues. I'd play it by ear and try to listen to my body. If you're body isn't in a situation where it will be able to recover from training, then there's not much use in doing it. A good example of that would be a stomach problem. If I can't get the nutrition I need to support my training, then there isn't much use in doing it at all.
Current PRs at 242, raw w/ wraps- 525, 355, 605, 1485
Roboro tui, perimo vester adversarius
(Build yourself, destroy your enemy)