I really prefer variations on the triangle over anything else.
I personally like Maui Jiu Jitsu's logo. They've incorporated a lot of things but kept it simple. It has a map of Hawaii, and a representation of Luis Heredia's 5-striped black belt surrounding a triangle done sort of 'island-style.' Classic.
Brazilian Jiu Jitsu in Maui, Hawaii
Stylistically, I'm not a fan of cartoon animals, even though I proudly wear one on my back. Just not what I would design if given the chance.
Kneebarcity, what sort of ideas are you looking at for your logo?