Most of the shows that I would recommend for the quality of their animation are not action shows. But in that genre I'll start with
Noein.
Episode Twelve contains one of the most remarkably animated battle sequences I've seen in an anime made for television. Unfortunately all the online versions only include the atrocious English dub, but the characters don't speak much during this sequence. It begins at around the 8:00 mark.
Seirei no Moribito has a few excellent spear-fighting scenes, but it's not really an "action" show. It's largely a political and supernatural drama set in a fictitious Asian empire. The best-known action sequences occur at the beginning of episode three and at around 17:30 of episode twelve. Director
Kamiyama Kenji has done some other well-respected shows like
Eden of the East and
GiTS:SAC.
In
Claymore, beautiful blonde women undergo a surgical procedure that implants demon flesh in their bodies giving them the power to fight those demons.
Claymore has an unsatisfying conclusion because the manga was still being written when the anime adaptation ended, but it tells a good story with strong characters. The "Teresa arc" which begins in episode five is especially powerful.
Claymore has many fighting scenes scattered throughout the series and a color palette that matches the dreary setting of this story.
I'll also recommend
Bakeneko, the third arc of
Ayakashi Samurai Horror Tales, and its sequel, the unlicensed
Mononoke. The art style of these shows mixes classical Japanese painting techniques with a psychedelic look that reminded me of
Yellow Submarine. All the shows appear to have been painted on parchment. There are five separate stories, each of which pits the main character, a travelling medicine seller, against a variety of demons. You can find these on YouTube, but the quality of uploads and streams don't do justice to the beauty of Nakamura Kenji's work. Nevetheless here is a
brief clip to whet your appetite. A subtitled rip of the Japanese Blu-ray re-release of
Mononoke resides on a well-known anime torrent site I cannot name here because it also contains licensed works.
Nakamura has made three other shows for the noitaminA slot, all of which are visually distinctive.
Next, for pure visual and imaginative brilliance, you must watch Iso Matsuo's masterpiece
Dennou Coil. In this original story, children live in a virtual reality world overlaid on the physical one and visible only with special
glasses. There are some remarkably animated battles that take place in the cyber world, especially in episode four. Iso, like
Noein's Akane, seems to have retired from the industry.
Puella Magi Madoka Magica is a deconstruction of the magical-girl genre with some spectacular animation by controversial director
Shinbo Akiyuki. It dominated the discussion on places like this when it was released in early 2011. One of his other recent works, the manga adaptation
Bakemonogatari, also has quite unique visuals.
Finally I'll suggest
Baccano! which has some extensive, and quite bloody, fighting sequences and an intriguing, though convoluted story set in America during the Prohibition era.