I take very little time off sick, if I get a cold I work through it (I've usually caught it from the kids anyway), luckily I have a cast iron stomach and don't seem to get tummy bugs. The only sick time I've taken in the last couple of years was a week off for tonsillitis/quinsy.
I had very few, maybe 5-8 single days in 6 years, but I did have two incidences of a whole week due to full on flu in the space of 2 years which was really unlucky as I'd only ever had it once before that point in my life.
I did have to go home from work after throwing up a couple of times (had been fine in the morning!)
I've not had a sick day for over 18 months now - prior to that I managed to pick up 3 stomach bugs (one from the children) over a space of 4 months for which I had 1 day off for each (started taking probiotics after the 3rd instance)
Most nannies understand that they need to try and work through most illnesses as being off work directly impacts their employer. I just try and have an 'easier' day where we'll be home based with maybe a bit more tv than usual if I'm particularly rough.