Naruto: 

When a newborn becomes the imprisoning container of a nine-tailed demon fox with enough power to level mountains or create tsunamis with a swish of a tail it seals the boy's fate and makes him an outcast among his own people. The mischievous boy seeks acknowledgement and respect first through pranks and trouble but then he enters Ninja Academy and things begin to change.

Both the manga and anime are filled with fantastic fighting techniques and amazing ninja abilities. The manga has 40 volumes with 383 chapters while the American version of the anime has 220 Episodes which tell the coming of age tale of Naruto Uzumaki and his friends. Mostly rated T for Teen due to content and animated violence but if you don't know anything about anime and manga you can at least look like you do by picking up the beginning of this series for whomever you have on your list that digs ninja and fantasy-based action series.

Bleach:

Ichigo Kurosaki has always been able to see ghosts, but this ability doesn't change his life nearly as much as his close encounter with Rukia Kuchiki, a Soul Reaper and member of the mysterious Soul Society. While fighting a Hollow, an evil spirit that preys on humans who display psychic energy, Rukia attempts to lend Ichigo some of her powers so that he can save his family; but much to her surprise, Ichigo absorbs every last drop of her energy. Now a full-fledged Soul Reaper himself, Ichigo quickly learns that the world he inhabits is one full of dangerous spirits and, along with Rukia--who is slowly regaining her powers--it's Ichigo's job to protect the innocent from Hollows and help the spirits themselves find peace.

The Counts: 

31 volumes, containing 278 of 304 released chapters of Manga.  153 Episodes and counting for the anime.

One of the strangest anime series I have ever seen but by and far one of the best as well. I have been slowly working my way through the series and it's brilliant. Strange and weird and fast-paced and story-driven it is now firmly in my Top 5 of all time with Cowboy Bebop and Samurai Champloo.

Rated T for Teen for animated violence and probably language if you get the original Japanese with subs. 

 Cowboy Bebop:

In the year 2071, the crew of the spaceship Bebop travel the solar system trying to apprehend bounties. In the slang of the era, "Cowboys" are bounty hunters. Most episodes revolve around a specific bounty, but the show often shares its focus with the pasts of one of each of the four main characters and of more general past events, which are revealed and brought together as the series progresses.

The series includes a good soundtrack of jazz and other types of music and many of the action and fight scenes are timed to the music making it more of a dance at times. This is my favorite anime of all time and I often go back and watch it from beginning to end. The series included 26 episodes (called sessions) and a feature length film titled 'Knockin on Heaven's Door' that runs 115 minutes. This anime may not be for everyone but it is my #1 of all time.

Probably rated T for Teen again due to violence and situations.

Aired in 1998-99 and voiced by some of the heavyweights in the voice acting who you will find familiar as they are in almost everything these days.

The series is unrated according to Amazon but I would suggest T for Teen for language, situations and violence.There is a lot of sword play in it.

Samurai Champloo:

Shinichirō Watanabe does it again with another 26 episode series (he also did Cowboy Bebop) but this one is in a totally different vein though there are some similarities between them.

The series is a cross-genre work of media, blending the action and samurai genres with elements of non-slapstick comedy. It is also a period piece, taking place during Japan's Edo period. The series is interwoven with revisionist historical facts and anachronistic elements of mise-en-scene, dialogue and soundtrack. The shows most frequent anachronism is its use of elements of hip hop culture, particularly rap and the music it has influenced, break dancing, turntablism, hip hop slang, and graffiti. The show also contains anachronistic elements from the punk subculture and modernism, but less prominently.

 Pokemon:

The Pokémon anime series and films are a meta-series of adventures separate from the canon that most of the Pokémon video games follow (with the exception of Pokémon Yellow, a game based on the anime storyline). The anime follows the quest of the main character, Ash Ketchu (known as Satoshi in Japan) a Pokémon Master in training, as he and a small group of friends travel around the fictitious world of Pokémon along with their Pokémon partners.

I needn't really even explain this series do I?  It is still around and evolving and changing. But the good part is that it's suitable for a slightly younger age range than much anime these days. Children from 10 years old could probably handle this as there is no fear of bad language and little actual violence.