Well, i had a century ride planned with a friend and when i woke up,i felt like total crap. Popped some pills and took off. On the way back in we had to stop every 5-10 miles because i was burning up and exhausted from fever. I made it the whole ride but i wouldn't recommend riding if you're that sick. It's miserable and you'd be much better off resting so you can recover quickly as possible and then ride.
If you have a cough or maybe a runny nose,then by all means,ride. But anything above that i wouldn't do.