Rubber
Leather
Cord/Half-Cord
Quick Comparison
Oversized/Undersized

Rubber
Rubber grips are made by adding granulated cork, as well as other materials in the liquid rubber. The "cork" serves to displace the rubber, and is the reason many grips are called "composition" grips. It also makes the overall weight of the grip lighter. The rubber/cork blend is checked to assure the proper viscosity, and is then molded in a high pressure molding machine. After molding, the grips are sanded and painted. Some of the features of rubber grips are: easy installation, "reminder ribs" for hand placement, and they are less expensive.

Leather
Most of the "stars" over forty use leather, while the younger players use various rubber molded grips. The reason has very little to do with the quality or playability of the grip, but simply a difference in what each generation has been accustomed to. One of the features of leather grips (generally made of cowhide or calfskin) is that they have a nice soft, pliable, tacky feel. A few of the drawbacks are its difficulty to install, and its price.

Cord/Half-Cord
Most of the more popular rubber models come in an optional "cord" grip, in which strands of fabric thread are embedded in the rubber grip. This makes for a better non-slip contact with hand or glove, especially when wet with rain or sweat. However, it does wear out gloves faster than non-cord grips. (Hands, too. :-)

Many of the "cord" models also come as "half-cord", in which the top of the grip (where your thumbs are) are smooth rubber and the bottom (where your fingers wrap around the club) are cord.

Quick Comparison

Rubber Grips

Slip-on design
Easy to install
Less expensive
Rough when corded

Leather Grips

Usually wrapped spiral design
Harder to install
More expensive
Natural soft, tacky feel

Oversized/Undersized
Grips come in a standard size, but can be padded to a larger diameter with tape on the shaft under the grip. It is also possible to get larger and smaller diameter grips. A few of the pros and cons:

Oversized

For larger hands
Minimize arthritis pain
Decreases hand action, promoting a slice

Undersized

For smaller hands (most women)
Increases hand action, promoting a hook