The Monk, whose true identity was Niccolai Tepes, was a vampire who fought Batman.
History
Behind the scenes
The Monk first appeared in Detective Comics #31 in 1939. He is one of the earliest significant villains of the series, his battle with Batman being one of the Dark Knight's first multi-part adventures. The Monk is a vampire who wears a red, monk-like outfit, with a hood that bears a skull and crossbones. He has an assistant named Dala who lures Batman to his lair using Bruce Wayne's fiancee, Julie Madison, as bait.
The Monk places Julie in a hypnotic trance. The Monk is killed by a lighting bolt and Dala dies by falling on her own dagger.
The Monk would return several decades later when writer Gerry Conway revived him in 1982's Detective Comics' #515. The Monk's appearance is preceded by Dala's return in Detective Comics #511, during which she romances Dick Grayson (a.k.a. Robin) as part of her master's plan.
Conway's story is ostensibly an update of the original tale, establishing an Earth-One counterpart of the Monk during the days of DC Comics' Multiverse. It departs from the original, however, by establishing the Monk's true identity and origin. In Conway's version, the Monk is a post-Civil War plantation owner in New Orleans named Louis DuBois. He and his sister Dala are attacked by their vengeful ex-slaves and subjected to a voodoo ritual which transforms them into the undead.
During the course of the story, Batman himself is transformed into a vampire by the Monk but is eventually cured by a serum administered by a priest/exorcist named Father Green. At the conclusion of the tale, Green departed with the captive Monk and Dala, hinting that he had been pursuing them for a very long time indeed.
Although later events have called this story into question, the Monk's continued existence in the post-Crisis version of the DC Universe was confirmed by the presence of a familiar red hood displayed as a trophy in the Batcave.
Batman and the Mad Monk
In the summer of 2006, DC began publishing a six-issue miniseries by writer/artist Matt Wagner called Batman and the Mad Monk. This is once again a revised update of the original Monk story.
In this version, the Monk is referred to as Niccolai and is the vampiric leader of a cult called The Brotherhood, based in an abandoned castle/manor house on the outskirts of Gotham City. His followers, among whom is the gothic Dala, feed upon the blood of captured victims. Only the most devoted acolytes are transformed into true creatures of the night however. Maintaining a link with the 1939 version, Julie Madison is once again turned into the Monk's pawn, as she is lured to the castle by Dala under the guise of the Monk being some sort of self-help guru. At present, the current origin of the character has not been revealed. It should be noted that Dala is not a vampire, but she hopes to become one so she can serve as Niccolai's right hand.