Judo and Taekwondo are probably the most popular ones. Wrestling is also practiced in just about every culture in the world.
Well let see just how impractical this is. There are around 75+ styles of Taekwondo, 50 or so styles of Karate, hundreds of styles of Kung Fu, there are at least 3 or 4 varieties of Taichi, several dozen varieties of Japanese Jujitsu, then there is the list that Jas Key gave you. I do have to disagree though, MMA and Kickboxing are sports that are open to competitors from any style of martial art.
Depends where you are at. In China more Chinese martial arts will be popular than in the US. In Japan, there will be more demand for Japanese style of martial arts. In the US and the West sports styles are popular, in fact they are so popular they have taken traditional styles and made them into sports.
First you have to define what popular is?
Well, this seems simple enough...
Tae Kwon Do, Hapkido, Karate, Judo, Aikido, Kendo, Taichi, Wing Chun, Shaolin, Muay Thai, Kali/escrima/arnis, Sambo, Wrestling, Krav Maga, Fencing, Kick Boxing, Boxing, MMA, Brazilian Juijitsu, and Capoeira.
I only listed ones pretty popularly practiced, but there are plenty more styles out there.
brazilian jiu jitsu all day. with some freestyle wrasssling
Just things like mma boxing kick boxing karate the more popular ones
