This article is from the Fitness FAQ, by Jeff Gleixner (glex@cray.com) with numerous contributions by others.
Generally if the sickness is above the neck, it's alright to
exercise (sinus, headache, sore throat, etc). Just take it easy
and respect others who aren't sick by wiping off the bar or
handlebars when finished and by washing your hands frequently
if your sickness is contagious. It might also be a good time
to take a few days off to let your body recuperate, getting sick
might be a sign of overtraining.
 
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