Having a below normal workout is better than no workout at all.
The only time I won't work out when feeling under the weather is if I have a high fever, feel sick to my stomach, or have a lower respiratory infection.
if I am having a crappy workout sometimes I just blow off the rest of the workout....I think this is no problem as long as it doesnt happen too often
i workout anyway. but sometimes maybe its better not to if your really sick. but i find it hard to skip a gym day
However if you are asking if you should workout when sick I would say it is up to you. I would venture to say that 5 years from now the workout you missed because you were deathly ill will be of no consequence. But I will make myself feel worse if I skipped a workout unless I was puking my guts out or something.
I dont care if i'm a shuddering, shivering, sneezing, hacking, incontinent typhoid-Judas, if i can still get PR's or do the weights i need to do, i'm there.