My favourite manga is either 'Hellsing' or 'Deathnote', But i think my favourite Anime has to be 'Claymore'

Hellsing is a 'Vampire-turn-vampire-slayer' kind of manga, really good with some awesome artwork.
Deathnote is about a student that finds a special notebook that he can use to kill people, kind of a crime/thriller style.
Claymore follow the story of a demon slayer, its sort of an action/horror.

Didnt want to type/give too much away but you can look them up if your intrested