It's like asking why there are so many kinds of music. Music connects with us on a very personal level, and we all react differently to different styles of music. Dance is a physical expression of what the music makes us feel. With so many styles of music, it's only natural that there will be a variety of styles of dance. Let's look at the Waltz styles we've been discussing.
International Style Waltz - If your first dance steps were anywhere outside of the United States, this is probably the style of dance you learned. International Style is the standard for partner dancing - whether social or competitive - around the world. I love International Waltz because it teaches precision of technique and impeccable partnering - it is truly where two people appear to dance as one, as the partners never separate from each other once the dance has begun. It is elegant, timeless, and truly beautiful to watch.
American Style Waltz - If the first thing you ever learned about Waltz was a box step, then you probably learned American Style Waltz, which, surprise, surprise, is the style of Waltz taught and danced in the United States. (International style is of course taught here as well, but typically as a competitive style - if you're going out social dancing in the U.S., you'll see American Style most often.) In American Style, the partners are allowed to separate as often as they (i.e. the leaders) wish during the dance. This makes it a very expressive form of Waltz. That box step may seem pretty sedate, but as you learn to 'dance outside the box,' you'll find that American Waltz is at its best when the partners are not only turning and traveling, but also dancing into and out of each others' arms, as in underarm turns and dynamic side-by-side moves. I love American Waltz because its open movement and picture-story lines make me feel like the ballerina that I'm not.
Country / Western Waltz - Not surprisingly, a C/W Waltz is danced to a C/W song written in Waltz timing. Its style is in keeping with the spirit of the other Waltzes (turning and traveling dance, characterized by rise and fall), with a couple of differences. One is the music - a C/W song and a Ballroom song are bound to sound different. Also, C/W Waltzes are typically faster in tempo than an American or International Waltz, but not as fast as a Viennese Waltz. And, on the social dance floor, it is highly progressive, meaning that it is moving strongly down the line of dance, turning or not, pretty much all the time. There is a sense of movement to C/W Waltz that is hard to beat.
Viennese Waltz - Very likely the oldest of the Waltzes, it is also the fastest. Reminiscent of stately ballrooms in the courts of kings, Viennese Waltz combines the speed of a roller coaster with the rotation of the big swing at the fair - only Viennese Waltz spins in both directions. Oh yeah, and it's traveling all the while. This is an advanced Waltz, and typically reserved for dancers who have already cut their teeth on the regular American or International Waltz. Viennese Waltz is not for the faint of heart nor the sloppy of technique. It takes a lot of hard work - both in training, and during the dance itself - to pull this one off. But boy, is it ever fun!
So that's my two cents - now go try a Waltz!