I usually get turn off by most battle mangas, mainly because most battle manga rely on flash and explosions. I don't mind cool or over the top fights, but I can't stand flashy fights. So in other words:
NO!
History's Strongest Disciple Kenichi
Bleach
My Hero Academia
AirGear
Reborn!
Pretty much any series that have flashy explosions and way over power characters. >:-(

The only manga series I read so far that have some pretty good fights are Hanma Baki , JoJo's Bizarre Adventure Part 4: Diamond is Unbreakable, TOUGH and Hajime no Ippo
Know any good series?

[img]http://i46.photobucket.com/albums/f103/kinglame/kaiji.png[/img]

All Rounder Meguru and Teppuu are the only ones I can think of right now.

EDIT: I like Shut Hell too.

Holyland suits your description

Holyland, Blood and Steel.

I like very much Tenjou Tenge too.

I know Tenjou Tenge was pretty popular at the time, but like Air Gear at the time, I never really gotten into the series. I'll admit Oh! Great has mad art skills but he lacks when it comes to story and action, personally.

[img]http://i46.photobucket.com/albums/f103/kinglame/kaiji.png[/img]

Holyland seconded, probably the best realistic battle manga

I'll add :

Kenji Great start, but for me it got very boring after a while (once he gets to China). The fighting scenes are good but then the author introduces Chi and things like that... A shame, worth a check though.

Gamaran It's mostly armed combat. All the fights are very technical, not the most realistic but still cool.

Garouden By the author of Baki, this is very similar but a little more believable.

Tekken Chinmi Rather old but still decent MA manga. It has multiple sequels. It's more focused on adventure than martial arts but I remember enjoying it.

Ultra Red It has a rushed/axed ending but despite that it's still a good battle manga if a bit short.

And since you don't mind combat sports you could check All Rounder Meguru (very good manga about mixed martial arts), RRR (boxing) and maybe Ashita no Joe (a classic manga about boxing, one of the inspirations for HnI)

Holyland, for sure. Really fantastic in all ways.

Kenji got really boring for me as well.

Gamaran is just bullshit-fight after bullshit-fight. "Here I go with my supernew technique, raaaaaaaaaaaawr!" There's absolutely no logic in neither story or action.

Everything Oh! Great does (Tenjou Tenge, for one) is OH SO BAD. He draws really well, but he has no sense in how to explain his vision to paper. Only thing enjoyable with his works is the borderline-hentai.

Ultra Red was pretty good, but it was ages since I read it, and my tastes have matured, so I can't say much more than that I enjoyed it at a time when I probably could've enjoyed Gamaran as well. You know, back when I was stupid and a japanophiliac.

And RRR was pretty good as well.

I'll fifth Holyland, it's really good.

Tiji-kun! also fits what you want, but sadly it is an axed manga that has a slightly rushed end. It was fairly well don though.

Feng Shen Ji has nice battles up to chap. 62 since that's where I kinda put it on hold so it may have gone the flashy route after that.

Sidooh is not really a battle manga but its action sequences are kinda awesome, Shuto Heru is similar (I'm of the belief that it's Shuto Heru and not Shut Hell).

Shoukoku no Altair is definitely not a battle manga but its battles have such beautiful flow.

Personally, I have to agree with Jooles about Gamaran, its battles are very Bleach like to me.

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I really liked Holyland. All Rounder Meguru and Teppuu are pretty good too.

You could also try out Karate Shoukoushi Kohinata Minoru.