The most commonly used rice in the US is called, well, American rice. Of course, like most things Americans produce now, this rice is grown with very little human interaction. The rice fields in the US are operated mostly by machines and people in aeroplanes. I suppose this explains the price difference between this variety and the Abrorio variety I mentioned above and below.
The Abrorio variety comes from the Po Valley in Italy. It is a short grain rice with a high starch content so it gets soft and sticky, a quality that American rice does not typically posses. Abrorio rice is good for absorbing flavor and therefore is frequently used in risottos. This little tid-bit has helped me understand why, when I try to make a risotto with American rice, it just doesn't taste the same. Apparently this is also the type of rice that is used in sushi.
My personal favorite is basic Brown rice. Brown rice is rice that has not had the bran or germ removed, which is the process white rice goes through to make it white. Removing these two layers also removes a good deal of the nutrients and fiber rice contains. The flavor of Brown rice is a bit richer and it's better for you, so if you're in pinch eat brown rice.
Aromatic rice is a variety with many sub-varieties. They all have a rich, nutty flavor. Think Basmati or Jasmine. Yummy.
Wild rice, as it turns out, is not rice at all. While it comes from the same family, it is a distant cousin of rice. It is an aquatic plant that, like rice, also grows in shallow water. As the name suggests, it grow in the wild and not on farms.
As it turns out, some rice is white, some rice is brown, and some rice is fancy.While there are about 1000 types of rice (this is not a real number just an exaggeration), I feel this basic knowledge will help me use rice to create better meals. Are there any questions?