Bakemonogatari's a new anime that started airing recently. The story is apparantly based on a set of light novels. The story's written like a set of supernatural mysteries that the main character, Koyomi Araragi, get thrust into.
The first two episodes cover the Hitagi Crab story, where Araragi catches a falling girl, noticing that she's extremely light. She later attacks him with various stationary, trying to make sure he doesn't tell anyone about her condition, and would probably have wounded him quite badly if it weren't for the fact that he used to be immortal, and thus heals back from injuries quite rapidly. Despite the attack, he offers to help her get herself cured of her weightlessness, and he takes her to a friend of his, Oshino, to see what can be done.
Being fairly unfamiliar with the original light novels, I'm not sure how Araragi cured himself of the vampirism that he had originally contracted (it was the source of his original immortality, which Oshino cured him of). It wasn't relevant to the story so far except as a premise for him to have met Oshino already, but it does raise a lot of questions about the setting that presumably will be answered over the course of the story.
The writing in the story so far is pretty good, and it has a few allusions and parodies of other series (Hitagi's harsh words are transmuted from various base elements and 97kg of spite!), and it's woven in well enough to not disrupt the story itself. The artwork is great, and it's very noticeably SHAFT's style, with their bright colors on drab backgrounds, and large amounts of text woven in to accentuate certain scenes and events. The music is fairly nice, though I'm unfamiliar with the musicians involved -- the two openings so far have been different, so if I'm lucky, maybe they'll have a unique opening song for each episode.
Seems like it's another anime I'll have to be following this season.