From what I've seen, you should definately check out Claymore and perhaps Tenjou Tenge
I love pretty much all the anime you listed :P
especially Hunterxhunter...even if the manga is way better IMO
you should check Dorohedoro, is a Seinen manga, really splatter, it has some funny moments but the plot and the characters are awesome! a very unique manga.
i got a few anime that you might like...try jigoku shoujo/hellgirl,and one piece...actually,one piece is not a serious anime...it's a funny and adventurous anime...but try to check it out first...
here is a list of shows that have a little of everything that you are looking for, so try, berserk (violence and demon blood orgy), when they cry (thriller, kind of creepy considering what is involved and that the character designs are kind of cutesy, really deceptive), shuffle! (way better then negima as a harem show to watch because its actually more dark and still funny to watch), and rahxephon (if you enjoyed NGE/Eva, then you will like this because it actually has an ending that you can see without getting a movie to tell you what happen in episode 25/26).
now it's me again...i have to you watch death note like everybody said in this thread...i just start watch this anime...its really amazing,plus it's suit with your serious type of anime...by the way try hellsing too...
Well if you like Neon Genesis Evangelion you will probably like Gundam Wing. If it is serious you want Rumbling hearts is pretty good and short. If you cannot get enough of ninjas teh very grown up anime Basilisk is for you.
you could watch Crest of the stars and banner of the stars I and II, Seikai trilogy i believe it was called... fairly serious but has some unique jokes in it.
Forgiveness is between them and god. It's my job to arrange the meeting.
I you need a laugh ' Hayate No Gotoku!' is an awesome anime that kind of touches your heart and fills it with joy and also gives you a good laugh all the way through it.
Also 'Fate/stay Night is a good Anime to watch if you like some action in it.