I actually intentionally ride when I'm starting to catch cold. It seems to kick my immune system into high gear. If I'm getting a little sick, all I have to do is jump on the bike and commute in, and it's gone.

There's been some speculation here that the cold weather stimulates massive mucous production, which tends to flush the airways.
As far as going to work when you're actively sick (transmitting germs, or with something serious like flu):