Bakemonogatari

First season of the Monogatari Series, part 1/6. Contains the arcs Hitagi Crab, Mayoi Snail, Suruga Monkey, Nadeko Snake, and Tsubasa Cat from the Bakemonogatari light novels.
Thanks to Meme Oshino, Koyomi Araragi, a high school student, is able to remain a human after coming across a female vampire... However, since the incident, Koyomi seems to meet girls who have an apparition-related issue. Hitagi Senjougahara doesn’t weigh anything, Suruga Kanbaru’s right arm becomes like that of a monkey’s, and a young girl, Mayoi, cannot find her way home no matter how many times she tries. Koyomi, a Mr. Nice Guy, ends up helping each and every girl solve her problem with the help of Meme Oshino.

(Source: Aniplex)
Note: Only the first 12 episodes were broadcast on television; the remaining three episodes were distributed on the anime's website between November 3, 2009, and June 25, 2010.