Shaking hands is a sign of respect, the absence of hostile intentions, trust and a promise of working together.
That being said, when I meet someone new for the first time, I always give them a firm handshake. In fact, the handshake tells you alot about another person.
Conclusion: it increases your social relationship especially when you meet someone new, and it also tells you alot about the other person in question.
Handshakes all the way, baby.