If you want to be somewhat original when shaking a girl's hand or anyone's hand for that matter try this:
When going in for the handshake extend your hand and take hers gently. Right before you take her hand have your left (or right) hand come over hers. Hold it there for an extra second and give her your killer smile and some nice eye contact.
I learned this from Trent in swingers and it has worked wonders for me. It shows confidence and you don't see most guys do it. It's different. I get positive reactions literally almost all the time.
Give it a try!