When you bring my coffee cup to the table, holding it by the rim with your fingertips, I'm hoping silently that you've recently washed your hands. Wouldn't it seem logical for you to hold the cup by its handle and not by the rim?
The same holds true for an iced tea glass, but at least with the tea I get a straw. It's really difficult to drink hot coffee through a straw.
So, especially during cold and flu season, or if you have a sniffle, or if you've not lately washed your hands in hot soapy water, or if, God forbid, you are an unknowing carrier of some hepatitus or other virus, Please, Please, keep your hands off the rim of the cup. I realize that in the Grand Scheme of Things this may seem unimportant. However, I really, really do not want your fingers in my mouth.