The first anime I ever got hooked on was Dragon Ball Z. Years later I would stumble onto DBZ Kai and have a "meh" view on it. Then I went back and watched the original and realized something. Kai has way more action. In the original, characters would usually scream at each for 3 episodes and then throw a few punches.
Since then I've acquired a taste for action and shonen anime, as well as a few others.
Darker Than Black
Tenjou Tenge
Naruto
Bleach
One Piece
DBZ
Kekkaishi
Death Note
and my all time favorite; Fullmetal Alchemist: Brotherhood
I have a bad habit of skipping story stuff in a few of the less interesting one to get to the fights.
Oh, I also like fighting Animes
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Hunter x Hunter is one of my favourites, especially because the characters become stronger along with the story
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You also might like D-Gray Man.
A manga (anime doesn't yet exist) highly focused on martial arts is "The Breaker". I'm a big fan of that one ^^
A quite recent anime is Shingeky no Kyojin (or similar) which has an interesting way of fighting, especially because the enemy are giants.
Since you liked Death Note I recommend you Codea Geass. It unifies (genius) strategical thinking with action scenes. The story is great and I found the ending fantastic (you have to watch both seasons).
And if you're into pure action with not that much of a story I recommend you Fate Zero. It has great animation and is quite short.
Another one might be Berserk. I haven't watched the anime but the manga was good and focused on ninja clans fighting each other.
I haven't seen the anime of it but I can imagine that Gantz has some fighting as well though its style is very different from what you're watching and the drawing as well as the story aren't what I'd define as common or normal. Also, the story isn't very easy but interesting, so skipping parts of it isn't recommended.
I hope you enjoy one of them if you ever look into it
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