For me, it depends on the sickness.
For
colds/flu, I will try to do as much of my workout as possible, depending on (a) whether or not I have fever, and (2) how much energy I have.
Any
fever is a sign to rest - and work on getting that fever down.
And if I have NO energy to work out, if my body is DEMANDING rest, then that's what I do. I rest. I eat chicken noodle soup, drink orange juice & lots of water (must stay hydrated!) and just rest/rest/rest. I kick it a lot quicker that way.
If I'm at the middle or end of a cold/flu, then I do what I physically feel like doing & stop when I feel too tired.
If I have
stomach issues (diarrhea, etc.) then I will usually do yoga because it is non-strenuous.
Cramps/headaches (likely cause: PMS)
Cramps: I go ahead & work out. Walking is very good for cramps. (But then, so is beer!

)
Headache: usually forgo a workout because any "rush of blood" to the head makes the headache worse.
Headache (migraine) - no, I do nothing but lay in the fetal position & beg for death's sweet release.
So in general, mostly I forgo my workout if I am sick. I try to listen to my body as much as possible & give it what it needs.