claymore is a tough one to get similar to it... and I like it too, I just watched it again too
I can only really think of and some are 'borderline' if you get me.
blood+,
dance in the vampire bund - vampires and werewolf story, pretty good in my opinion.
rozen maiden (the original, not the remake) - yes it's magical dolls but seriously it's got a fantastic musical score and in my opinion a great plot.
mirai nikki (aka the future diary)
deadman wonderland - maybe not the gore (I can't remember it being too gory but others are saying it is...) but it covers the rest ok
elfen lied - you want gore you say....watch this... although it does have some nudity too.
shiki - newbie in mysterious town etc
another
dusk maiden of amnesia
black lagoon - not exactly special powers but if you're like me you'll like this, it would be in my top 10 with claymore, eureka 7, rahxephon and fate stay night... all of which are good too by the way
edit: forgot about gantz