Guess work on my part, but I agree with the previous posts.
Given the size of the country and the presence of wushu on the school curriculum China probably has the largest in raw numbers, and percentage of population given that both men and women are able and are encouraged to practice wushu in school. It does depend how one views performance wushu, and school age training.
I reckon it is safe to say that it is easily China that has the highest raw numbers and percentage of martial artists studying both at school age and in old age, given the presence of wu shu on the school curriculum and the popularity of Tai Chi and Qui Gong exercises in later life.
I would say South Korea has the highest percentage of "fighting" martial artists per male head of population. Military service is compulsory for all men, and a form of Taekwondo is part of a conscripts training. North Korea may even be higher, but as it is a closed country it is hard to know. I doubt many Koreans continue their training after 3 years of military service, from the few people I spoke to it wasn't the most popular aspect of their time in the military. 50% of the population drops out of the calculation though, as women aren't conscripted in South Korea. Policemen and women are likely to practice at least one martial art though.
Although martial arts are probably not as popular as may be stereotypically believed; I reckon Japan scores reasonably highly as both kendo and Judo are very popular school sports, with kendo being widely practiced by girls. Baseball and soccer rank first and second as sports for boys (soccer might actually be the most popular now). Outside of the police forces and university clubs aikido and karate seem surprisingly rare. (Just personal impression, not hard stats though)
Not on the list, but I reckon Thailand, Laos, Burma would rate rate pretty high as Thai/Khmer boxing is pretty widespread there. Pol Pot did a lot of damage to martial arts in Cambodia, so I would expect they are actually quite low on the list now. The Phillipines should also score pretty well, as learning to fight from "uncles" is apparently a common tradition in the Philippines and still something of a practical survival skill in parts.
I definitely reckon the US and Canada will not be far behind when fencing, wrestling, boxing etc are taken into account (I wonder if lacrosse should count, it is arguably a traditional native American/Canadian martial sport?) China probably still has the overall top spot given the numbers of women that train.
I wouldn't expect Europe to score as highly as the US or Canada as wrestling is not a major sport. Popularity of asian martial arts is probably roughly the same.
Frankly I reckon these are "guesstimates" at best, but I reckon those countries that have a tradition of women studying martial arts as well as men will definitely be way up the list. It would be interesting to see if someone out there has some hard stats on the subject.
Dan:asian: