from Wikipedia:
ARGENTINA:
Esgrima Criolla
(plus many contemporary systems like Shinshinkan Karate, Ketsugo etc.)
BOLIVIA:
tinku/tinkuy (although more of a ritualistic combat)
(again other modern systems like Te Sat Tao and Shito Ryu Oshima Kai)
BRASIL:
Capoeira (regional, angola and contemporanea styles)
Vale Tudo (although is it really a martial art or a general term for no holds barred???)
Maculele (stick dance typically thought along capoeira)
Tayando and Kombato are both brazilian combatives/military martial arts
Luta Livre (wrestling)
and Brazilian Ju Jitsu (gracie, machado, etc.)
COLOMBIA:
Grima or machete fencing school, lotsa polemics on this systems but I found some videos of youtube (
)
EQUADOR:
Jutekwon a modern hybrid
PERU':
Rumi Maki (Inca) old martial art comprehensive of systems such as “Luchas de Tocto” in Chumbivilcas, the “Ch΄iariaje” in Cuzco and the “Lucheo” in Ayacucho and Tinku from Bolivia. I was hanging at browsing through the martial arts section in a Barnes and Noble and it seems like there is a book out on this art.
Vacon is another system or indigenous martial art mixing ju jitsu and street fighting techniques from the shantytowns on the outskirts of Lima
VENEZUELA:
Garote Canario/Juego Tucuyano
Makana Karive, don't know much about the style
that's all the ones I know about unless you want me to include the martial arts of Mexico, Central America and the caribbean