It depends... you looking for blood as in gore/horror, or from classic fight scenes?
Either way, check these out:
CLAYMORE
In a world where monsters called Yoma prey on humans and live among them in disguise, humanity's only hope is a new breed of warrior known as Claymores--silver-eyed girls who have willingly become half monster to destroy the predators. But the more the Claymores call on their supernatural strength, the closer they come to losing their human sides forever.
http://www.animenewsnetwork.com.au/encyclopedia/manga.php?id=5743
RUROUNI KENSHIN
During the violent era known as the Bakumatsu, there was an Ishin assassin known only as the Hitokiri Battousai, whose skill and brutality became near legendary in the age of Restoration he helped to build. However, as the time of fighting drew to a close, he vanished without a trace, only to resurface eleven years later as a wandering swordsman, Himura Kenshin. Now staying at a kenjutsu dojo maintained by a fiery-tempered woman named Kamiya Kaoru, and surrounded by newfound friends like the streetfighter Sagara Sanosuke, ex-samurai's son Myoujin Yahiko, and the shrewd doctor Takani Megumi, he seeks to carry out his vow to protect the weak without killing in order to atone for the lives he's taken. It's not long, though, before this vow is put to the test, and the shadows of his past return to haunt him and everyone he holds dear.
http://www.animenewsnetwork.com.au/encyclopedia/manga.php?id=1995
ELFEN LIED
The Diclonius, a mutated homo sapien that is said to be selected by God and will eventually become the destruction of mankind, possesses two horns in their heads, and has a "sixth sense" which gives it telekinetic abilities. Due to this dangerous power, they have been captured and isolated in laboratories by the government. Lucy, a young and psychotic Diclonius, manages to break free of her confines and brutally murder most of the guards in the laboratory, only to get shot in the head as she makes her escape. She survives and manages to drift along to a beach, where two teenagers named Kouta and Yuka discovers her. Having lost her memories, she was named after the only thing that she can now say, "Nyuu," and the two allow her to stay at Kouta's home. However, it appears that the evil "Lucy" is not dead just yet...
http://www.animenewsnetwork.com.au/encyclopedia/manga.php?id=4233
Vampire Knight by Matsuri Hino
Its supernatural/romance themed.
Its got bloody bloody bite scenes.
ya can read at http://www.mangareader.net/104/vampire-knight.html ^_^
