Based on pre-ATS belly dance, particularly American Cabaret, Hahbi'Ru performs a kind of "Folkloric Tribal."
American Tribal Style
FatChanceBellyDance. Our dance mommas.
BlackSheepBellyDance at Tribal Fest 2007.
Disclaimer: "Cabaret" is a very broad term, and there are subtypes of cabaret, just as there are subtypes of tribal. Here are some of my favorite cabaret performances on YouTube, but this list is absolutely by no means exhaustive.
Aziza. Aziza performs American/Egyptian cabaret.
Shems (Performing to Oum Kalthoum's "Lissa Fakir"). And performing a rockin' drum solo.
Jillina. If you can ignore the pink snake costume, you can see she's really amazing.
Improvisational Tribal Style: Still using a system of movements and cues, these groups have developed a unique dance vocabulary with ATS as its base.
Unmata performing their high-energy improv.
n.o.madic tribal in 2007.
Tribal Fusion (Various)
Rachel Brice at Tribal Fest in 2006.
Urban Tribal Dance Company (they verge on just being dance fusion).
Ultra Gypsy in 2001.
Bellydance Fusion (Not Necessarily Tribal)
Mira Betz fuses the dignity of tribal with the grace of classic cabaret. Putting her in a category is very difficult - and I think that's what makes her one of my favorites.
Anasma. Theatrical fusion.
Hip Hop fusion by Raqs Arabi, directed by Crystal Silmi.
Sera and Solstice at Night of 1000 Goddesses, September 2007. They also perform tribal fusion.
In addition to these videos, Shems has an excellent article on her website on the different styles of bellydance with YouTube playlists for each. I encourage you to check it out.