There are two primary species of coffee grown commercially, Coffea arabica and Coffea robusta (or canephora). Both are members of the Rubiaceae family, the Madder family. C. arabica is native to East Africa and the Arabian peninsula-- hence the name "arabica." It is known for its splendid quality and comparatively smooth flavor.
Coffea robusta, also referred to as C. canephora, a West African native, is a much more robust coffee, as the name implies, that has a more earthy flavor and higher caffeine content.
Unripe C. robusta berries.
Today, C. arabica dominates yields in central and Andean America, along with East Africa. C. robusta is dominate in West Africa and Southeast Asia. Countries such as Brazil (which, incidentally, is the world's leading producer) grow both.
This map illustrates current coffee production by species: r (dark green) is C. robusta, a (yellow) is C. arabica, and m (light green) is both species.
The C. arabica of the East African nation of Ethiopia are my personal favorite. It is rather interesting to see the steps in the production of coffee, and this video clip presents it as it is in Ethiopia:
Of course, the cultural history of coffee as a drink is another interesting aspect. Originally, coffee seemed to have been perceived as an Islamic drink. Later, coffeehouses had quite the reputation for sedition and the spread of radical ideas. Worthy of note, too, is the story of the Capuchin friar, Blessed Marco d'Aviano, the chaplain of the Christian relief army at Vienna in 1683AD, who supposedly created cappucino from captured Ottoman coffee.
If you are looking for some excellent coffee, and a worthy group to purchase from, you can't do much better than Mystic Monk Coffee: http://www.mysticmonkcoffee.com/store/storefront.php