Rolling papers can be made from a variety of materials. The first rolling papers were most likely made from wood pulp — that is to say, the same material as ordinary paper — but as early as the 19th century, other materials, such as rice-based paper, were used. Each sort of paper has its own advantages and disadvantages, and of course any of them will do the trick. It really comes down to personal style. Still, for your reference, here's a quick look at the characteristics of most of the major rolling paper materials.
Wood pulp paper is probably the most common material for rolling papers. It's also the material used in factory-made cigarettes, so if you're used to smoking those, wood pulp paper may provide you with the most familiar smoking experience. If the rolling paper is made from wood pulp and it's white, that means its color has been altered, usually by the use of bleaching chemicals (e.g. calcium carbonate). For those who prefer their papers free from chemicals, natural wood pulp rolling papers are also available. These are usually light brown. Wood papers burn faster than some other types of rolling paper, such a rice-based papers.
Rice paper is almost exactly what it sounds like. It's made by processing rice and then pressing it into thin sheets. Some rice papers are made from all natural ingredients, and some may include various additivies. One advantage of rice-based rolling papers is that they can be thinner than traditional paper, and also burn slower. Some papers (and low-quality tobaccos) burn so quickly that the cigarette is done surprisingly soon. Rice papers can be tricky for those not used to rolling their own cigarettes, though, since the paper is low-friction, and so does not grip well.
Hemp rolling paper is growing in popularity. The paper itself has a pleasant, non-intrusive taste (though this effects the taste of the tobacco only marginally). It has a good grip, making it comparatively easy to use in rolling. An added benefit, for the environmentally conscious, is that it is made from the hemp plant rather than from trees.
Finally, there are transparent rolling papers like Glass and Trip Papers. Transparent rolling paper is made mostly from natural plant cellulose, but also contains a small amount of glycerin and water. It's a nice, organic material, is completely biodegradable, and does not require any glue or gum to be sealed -- all you have to do is wet the edge and it will seal easily enough.