I like the fist bump, and have been using it for a while since I'm so street you know...
But there are times when you just have to shake someone's hand. Entering a big business meeting or sale? Bumps not going to do anything there.
I think the handshake could be lessened, minimized, but it will always be needed. Also, as was mentioned, we've recently changed how we sneeze (into the crook of your elbow, instead of your hand) so that probably helps a lot.
As has also been mentioned, not only is it impossible to live a completely sanitary lifestyle, you wouldn't want to. It would kill your immune system. You gotta get in there and get dirty every once in a while. In fact, there are more and more studies coming out recently that is showing our city sanitary lives is probably what's causing this huge uptick in allergies, especially peanut allergies. Kids need to get out and get messy. It's good for them.