I have seen a couple different ways; I know the one where your thumb and forefinger are gripping the blade is popular, but i just wrap my whole hand around the handle and this is how i've always done it. Should I try this new way, or stick with what I know?
When I first started I was told to hold a knive as you hold a hand in a handshake. I find myself switching between the two, depending on what I'm cutting and how I'm cutting it. Its best to hold it as you feel comfortable.
Try the alternate grip when preparing some veggies; you may discover additional dexterity that you thought you never had. I myself use the alternate grip more frequently except when slicing bacon off of the slab. Then, I grasp the handle firmly to slice with raw alacrity.
I'm assuming we are talking about a chef's knife here.
Good knives and especially those with forged blades (as distinct from stamped) are balanced at the bolster. And that is why the thumb and fore finger grip the blade; your hand is right at the knife's center of gravity. It gives you better control over the blade and causes less strain on the wrist. (The knife is out of balance if you only grip the handle.) The down side of that technique is that the back edge of the blade rubs against your index finger and causes blisters until you develop a little callus there.