Here are a few of the most common, uniquely american belly dance styles:
The first is known as cabaret or egyptian. Thought to derive from the original middle-eastern dancers that first brought the dance form to the US. From the 20's-70's this is most likely what you think of as "belly dance". Aziza is a very well know practitioner. It is also my instructor Sonya's preferred style so I'm sharing one of her videos of course!
American Tribal Style (ATS) was supposedly started with the troupe Fat Chance BellyDance out of San Francisco. It takes belly dance moves and incorporates native american and other american dance styles. The costuming is distinctive with big full skirts often with harem pants underneath.
ATS has now evolved into tribal fusion which has many different facets from incorporating indian movements, to pops and locks from hip hop, modern dance, jazz and club. This video opens with a solo from the headliner of the show I saw last week, Mardi Love.
This is just a brief introduction to a few of the styles out there. Hope you enjoy them!