Some I've seen that has I've been pretty put off by - sanitizing one's hands after shaking hands. I'm not sure that this is a common place thing to do, but I've encountered it once and apparently our current President practices it.
Let me say that I get not spreading germs. I'm for staying healthy. But before you shake and sanitize, please stop to consider what kind of message you're sending. Whatever good you did with a great handshake, you just nullified and them some by washing up afterwards.
There are appropriate times to wash your hands. After using the facilities and before eating come to mind. Washing after shaking hands with someone falls into the category of the galactic faux pax.