At the cat rescue, we wash our hands before going from room to room. When we clean, treat and socialize with the kitties that are in cages in quarantine or sick bay area we wash/santitize our hands between each cage. If we take cats out to love, give medication, weigh, etc we put a towel on and then discard it/put it in the dirty laundry basket so we don't pass on germs. The cats there get Lysene every night with their supper - which is an immune system booster.
Some of the cats are FIV +, have a severe cold, or some have just arrived and we have no clue what to expect until their test results arrive so we certainly don't want to pass anything along.
Needless to say that we never play with our hands in order to avoid getting scratched - which happens some times anyway. And when it does we wash the scratch thoroughly, run it under warm water, put bandage on with neosporine right away so we don't get Cat scratch fever - like Tim mentioned.
I had cat scratch fever and it is very painful. It had to be operated on. It was over $900 - thank goodness I had insurance
But don't panic - you don't get that very easily unless you are very sensitive to it. I had rescued 13 kittens at once at the time and while being too small and with diarrhea had to wash their bottoms a lot in the beginning. They clinged on to my hands pretty tightly while I was taking care of their little rears
. I have amazing memories and would do it again any time!