While Japan has many homegrown martial arts styles, the show that is in the spotlight today is focused on boxing - so not that much of a cultural barricade (besides the one between Boxers and normal humans).
Hajime no Ippo (aka The Fighting or Lets go Ippo)
("It's the eye of the tiger, it's ..." )
The show centers around a boxing gym and Ippo, the protagonist that you just have to love. Instead of a silly "i want to get stronger" stereotype or something like that, Ippo mostly starts boxing because he's curious.
Just like our hero, the rest of the cast is well fleshed out and one of the big strengths of the show is the constant joking, bickering and pushing of the guys in the gym. Anyone who has ever trained in a good gym will immediatly recognize the atmosphere and it makes the show at least partially a comedy.
The other great strength are the fights themselves. Most fights get a buildup, but never too long. The fights themselves are designed almost like thrillers or chess matches, with strategies, sudden reservals of fortune and a great eye for what makes a fight interesting (This is probably where Naruto copied some of its more well-written fights).
(What also makes the show great)
This anime is also absolutly great when you don't watch sports anime because it works like an excellent action (or shounen) anime. The animation is ok at first and gets better and they also invested the largest amount of the budget into the action scenes.