From Chapter 24 of Tacitus' Germania
"[The Germans] have only one kind of show, which is performed without variation at every festive gathering. Naked youths, trained to the sport, dance about among swords and spears levelled at them."
In Capoeira, there are a few dances that we perform, either in honor of the African gods or the African slaves. The main dance is Maculele, where you will either see machetes or short wooden sticks (about the size of kali sticks) used. This is a recreation of African stickfighting and/or dance between two Capoeiristas. The other dance performed is called Puxada de Rede, which is the fisherman's dance.
The other type of dance is called Samba de roda. This involves both men and women in the roda, or circle. While Capoeira music is played, men and women dance in the roda, and if another man wants to steal a woman away from some other guy during the Samba dance, he can perform a footsweep to take out the female's partner. It's funny, because for something so fun, it can turn ugly between two guys fighting over a girl, and the girls love it. Just part of the Brazilian culture I guess. :)
Takedown
I thought that there is a type of "northern" Chinese lion which looks pretty different. The one with shaggy red fur I think ? If you watched Once Upon a Time in China 3 (aka Wong Fei Hung..) you can see pretty much every type of lion known to man.
Of course, Chinese opera has a lot of martial dance. Jackie Chan was originally trained in it.
I think some southern CMA performed their forms to music (drums, mainly) traditionally. At least for performance. Would that count ?
I think that, as IronMonkey pointed out, it really depends on the definition of martial dance that you adopt. I've done a little research on this topic since I made the first post, and I've turned up a LOT of different martial dances, but very few of them satisfy the original definition that I posted: Capoeira, Gatka, Krabi Krabong, and a very old form of Egyptian stickfighting called Tahtib are the only ones that seem to emphasize that rhythmic, interactive spontaneity that I was looking for.
If you allow group dances, or choreographed dances, or dances without music, the field opens up.