In Anglophone countries, shaking hands is considered the standard greeting in business situations. In casual non-business situations, men are more likely to shake hands than women. It is considered to be in poor taste to show dominance with too strong a handshake; conversely, too weak a handshake (sometimes referred to as a "limp fish" or "dead fish" handshake) is also considered unseemly.
There are various customs surrounding handshakes, both generically and specific to certain cultures:
1) Generally it is considered inappropriate to reject a handshake.
2) In some cultures people shake both hands, but in most cultures people shake the right hand.