What are your tolerances for violence? I would recommend Hellsing OVA but it might be too violent for you.
Lets see...
Action: Lots of this, but be warned that it is very bloody.
Adventure: I'm not to sure on the definition of 'adventure' in this context...but it isn't like, for example, One Piece.
Humour: There's some off-the-wall humor and the whole thing doesn't take itself too seriously. Edit- I should add that most of the humour is very dark.
Mystery: A little bit of this, but not much
Horror: Vampires, insane priests, ghouls (and later...) werewolves, illusionists, mad scientists, Schrodinger's Cat(boy), Nazi Vampires. I think this category is in the bag.
If you decide to check this one out, don't go for the original anime (thirteen episodes, completed) as, while it is good for the first half it falls apart in the second due to not following the manga.
The new OVA (two 40-50 minute 'episodes', ongoing) is much better, although they only seem to release a new episode every 6 months or so. Currently only subs of this are available. The first two episodes of this cover the same ground as the first half of the original anime. After this they should begin to diverge.
As I said before, it is very violent, so take that into consideration.