Ten most popular Manga: Based on World-Wide Sales!
1 Death Note
The main character is Light Yagami, a high school student who discovers a supernatural notebook, the "Death Note", dropped on Earth by a death god named Ryuk. It centres around Light's attempt to create and rule a world cleansed of evil using the notebook and the efforts of a detective known as L to stop him. The Death Note grants its user the ability to kill anyone whose name they know, by writing the name in the notebook while picturing their face. It ran for 12 Volumes from 2003 - 2006 and, in many fans opinions, remains so popular because it ended at the right time; before it got tired and outstayed its welcome.
A Volume 13,
Death Note: How To Read, an encyclopedia-like guide to the Death Note manga series, including character bios, storyline summaries, interviews with creators Tsugumi Ohba and Takeshi Obata, production notes and commentaries, and a bonus: the pilot chapter of the manga, was published in 2008. And a light novel:
Death Note Another Note: The Los Angeles BB Murder Cases, published in 2007.
Both proved immensely popular among fans
2 Naruto
Is an ongoing Japanese manga series written and illustrated by Masashi Kishimoto. The plot tells the story of Naruto Uzumaki, an adolescent ninja who constantly searches for recognition and aspires to become a Hokage; the ninja in his village that is acknowledged as the leader and the strongest of all.
The series is based on a one-shot comic by Kishimoto that was published in the August 1997 issue of
Akamaru Jump. The manga was first published by Shueisha in 1999 in the 43rd issue of Japan's
Weekly Shōnen Jump magazine and the story has not yet reached its end.
3 Bleach
Bleach follows the adventures of Ichigo Kurosaki after he obtains the power of a Soul Reaper—a death personification similar to the Grim Reaper—from Rukia Kuchiki. These abilities force him to take on the duties of defending humans from evil spirits and guiding departed souls to the afterlife.
Bleach has been continuously serialized in the Japanese manga anthology
Weekly Shōnen Jump since August 2001, and has been collected in 45
tankōbon volumes as of June 2010. Since its publication,
Bleach has spawned a substantial media franchise. The manga has been adapted into an animated television series produced by Studio Pierrot which is still ongoing in Japan as it adapts the story from the manga.
4 Fruits Basket
Fruits Basket, sometimes abbreviated
Furuba, is a Japanese manga series by Natsuki Takaya. It was serialized in the semi-monthly Japanese magazine
Hana to Yume, published by Hakusensha, from 1999 to 2006. The series was also adapted into a 26-episode anime series, directed by Akitaro Daichi. The series tells the story of Tohru Honda, an orphan girl who, after meeting Yuki, Kyo, and Shigure Sohma, learns that thirteen members of the Sohma family are possessed by the animals of the Chinese zodiac (十二支,
Jūnishi?) and are cursed to turn into their animal forms if they are embraced by anyone of the opposite sex. (Though at least by the anime it's more of just torso to torso touch that activates it.)

5 Fullmetal Alchemist
is a Japanese manga series written and illustrated by Hiromu Arakawa. The world of
Fullmetal Alchemist is styled after the European Industrial Revolution. Set in a fictional universe in which alchemy is one of the most advanced scientific techniques known to man, the story follows the brothers Edward and Alphonse Elric, who want to restore their bodies after a disastrous failed attempt to bring their mother back to life through alchemy. The manga was serialized in Square Enix's
Monthly Shōnen Gangan magazine starting August 2001 and ending June 2010 has 25 volumes.

6 Love Hina is a Japanese manga series written and illustrated by Ken Akamatsu.
It was originally serialized in
Weekly Shōnen Magazine by Kodansha from October 21, 1998 to October 31, 2001 and was published in 14 volumes by Kodansha.
The series tells the story of Keitaro Urashima and his attempts to find the girl with whom he made a childhood promise to enter the Tokyo University.

7 Rurouni Kenshin Rurouni Kenshin: Meiji Swordsman Romantic Story also known as
Rurouni Kenshin and
Samurai X, is a Japanese manga series written and illustrated by Nobuhiro Watsuki.
The fictional setting takes place during the early Meiji period in Japan. The story is about a fictional assassin named Himura Kenshin, from the Bakumatsu who becomes a wanderer to protect the people of Japan. Watsuki wrote this series upon his desire of making a
shōnen manga different from the other ones that were published in that time, with Kenshin being a former assassin and the story taking a more serious tone as it continued. Although the tragic tone was highly expanded as the manga advanced, Watsuki became determined to give it a happy ending as it was aimed at teenagers.
The manga initially appeared in Shueisha's
Weekly Shōnen Jump from September 2, 1994, to November 4, 1999. The complete work consists of 28 volumes, while years later it was reprinted into 22 volumes.

8 Berserk Berserk is an ongoing, long-running dark fantasy manga series written and illustrated by Kentaro Miura. The first volume of the manga was published on November 26, 1990 by Hakusensha in its Jets Comics collection.
Berserk's setting is inspired by medieval Europe. It centers around the life of Guts, an orphaned mercenary warrior, and Griffith, the leader of a mercenary band called the Band of the Hawk. As he ages, Guts changes from a solitary boy into a man who realizes the value of camaraderie. The story contains elements of both fantasy and horror, as it explores both the best and worst of human nature. Both the manga and anime are noted for their heavy violence.

9 Chobits Chobits is a Japanese manga created by the Japanese manga collective Clamp. It was published by Kodansha in
Young Magazine from February 2001 to November 2002 and collected in 8 volumes.
The series tells the story of Hideki Motosuwa, who finds an abandoned
persocom, or personal computer with human form, that he names "Chi" after the only word it initially can speak.
As the series progresses, they explore the mysteries of Chi's origin together and questions about the relationship between human beings and persocoms.

10 One Piece
One Piece is an ongoing long-running shōnen manga written and illustrated by Eiichiro Oda, that has been serialized in
Weekly Shōnen Jump since August 4, 1997. The individual chapters are being published in volumes by Shueisha, with the first released on December 24, 1997 and the 58th volume released as of June 2010.
In 2009, Shueisha announced that they sold 176 million volumes of
One Piece manga so far; volume 56 set a new record for the highest initial print run of any manga in history.
One Piece follows the adventures of Monkey D. Luffy, a 17-year-old boy who gained incredible abilities by eating a magical fruit known as a Devil Fruit, and his ragtag crew of heroic pirates, named the Straw Hats. Luffy's greatest ambition is to obtain the world's ultimate treasure, One Piece, and thereby become the next Pirate King. From islands of giants, islands in the sky, islands permanently covered in snow and even islands underwater, the One Piece Universe is a place full of mermaids, fishmen, giants, angels, cyborgs, zombies and many MANY people who have gained different powers by eating of the Devil Fruit. Men made of rubber or fire, men who can turn into dinosaurs or even animals who can turn into humans, the One Piece universe has no limits when it comes to wonders of the imagination.

I read Death note and One Piece myself. Nothing else on this list has ever caught my interest. I also read Dragon Ball, and will be moving onto Dragon Ball Z when I've finished that one.