Sick Days

While people who bike regularly tend to have overall better health (and, as you can point out to your boss, take fewer sick days on average than more sedentary employees), sometimes you just get sick.
Days like that, you just have to ride a bit slower, or maybe just stay home, there's rarely anything to gain by pushing through it. If you have to go anywhere, dress warmer than the weather would normally warrant and drink lots of water.
One noteworthy "illness" which seems to clear up more quickly with gentle exercise is a mild to moderate hangover. Again, drink lots of fluids and go slow, but if you can get moving, working up a bit of a sweat clears out the remains of your overindulgence pretty handily sometimes. Also, say you drove to the bar on Saturday night, but had to take a cab home, riding your bicycle back to where you left your car will (um... so I've heard).
Of course, if you're a bike blogger and you're feeling under the weather, it's also a good excuse to deliver a shorter-than-usual post.