The majority of golfers putt with a conventional grip. That is, they putt with the same grip they use in the full swing: left hand on top, right hand on bottom. The benefit of using this technique is that there is no variation from a golfer's normal grip. Most golfers just feel more comfortable using a conventional grip.
Many PGA Tour players use a reverse overlap grip. The reverse overlap is similar to a conventional grip, except for one variation. In a reverse overlap, you extend your left index finger so that it wraps around the fingers of your right hand. The supposed benefit of this grip is the feeling that your hands are closer together, that they move as a unit.
Cross-handed putters stroke the putt with their right hand above the left. This grip levels your shoulders. Players who use a conventional grip have a slight tilt to their shoulders. Players also feel the cross-handed grip helps them keep their wrists firm through the stroke.
Belly putters are much longer than traditional putters. A golfer can anchor the top of the belly-putter shaft in his belly. With the putter anchored in your belly it can be swung like a pendulum. Belly putters are popular among golfers who tend to use their wrists too much. With the belly putter, a player can take the worry of too much wrist action out of his stroke.
A long putter is the longest putter available. It's so long, the putter grip actually rests in your sternum. Long putters provide the same pendulum action that belly putters do. The putter stays anchored in your sternum throughout the stroke. Players who use a long putter tend to stand taller than players who use a belly or conventional putter.