I must be in the minority on here, because I have no problem with shaking hands. And over the years, I learned how to give firm handshakes that people respect. I reached a point where I'll think higher of a person giving a good, firm handshake, even when that person is a woman (who generally, although not always, give lighter handshakes). Of course, the opposite is equally bad. When someone almost crushes my hand, I can't help but think: "Overcompensating much?".
I really like the history behind shaking hands. It's believed to have originated in ancient Greece. Back then, you generally trusted no one, and most men always had a weapon ready. Since most people are right-handed, they carried it in their right hand. So when two strangers met, it was expected that they were both armed. But when you extended your bare hand to a new person, you were demonstrating that you were not holding a weapon because you trusted him. He was expected to do the same in return. 5,000 years later, people still shake hands, even though almost no one carries a gun in their hand at all times.