Sheets and pillowcases
Changing the sheets after you've been sick is a good thing to do for the obvious reason that you've probably spent an extended time lying there, breathing germs all over the place, sweating out a fever, and generally doing all the gross things that sick people do. The other reason to change your sheets after you've been sick is that getting into a freshly made bed when you begin to feel better sends a psychological signal that you're feeling much, much better.
If your illness is dragging on and you can't muster the energy to strip the bed and launder a full set of sheets, you might want to consider changing the pillowcases as a half-measure. The cases, after all, bear the brunt of your runny nose and sweaty brow. As a bonus, laying your weary head on a clean pillowcase will probably help to make you feel a little less gross.