Rice is not a New World food. Rice was introduced to Mexico via the Philippines, then transported to Acapulco in the famous ship Nao de China (Diana Kennedy, Art of Mexican Cooking).
The Spaniards later found the lush tropical climate of Veracruz region of Mexico to be a perfect growing ground for rice. From there it grew to culinary prominence.
Rice is traditionally served as the second course of the midday meal. It may be served turned out of a mold to be eaten with beans or with fish. The serving of "rice and beans" next to each other on a dinner plate is not at all typical in Mexico.
Rice is not only reserved as a savory dish but it is also used in desserts, cakes, vegetable puddings, tamales, atoles and even the well known rice drink, horchata.
The rice most commonly used in Mexico is a long-grain with a fleck of the germ left on. When cooked the rice expands to 4 x's its volume. The long grain rice found in the U.S. is really not the same. Both Rick Bayless and Zarela Martinez recommend using a medium-grained white rice for best results.