Another member with "Storm" in their name, it is indeed good to see it!
Other then my obligatory
"Watch Clannad" choice, it is slice of life, but it can pretty but kill your heart from some of the scenes. A good romance, tragedy is what I would say.
Seemingly enough, not your thing, understandable. [sub][sub]seriously go watch it when you want to.[/sub][/sub]
BUT, more into your tastes. I have marked those that might be in your area with smaller text.
Hellsing Ultimate - Blood, supernatural and very large guns. Heck it is even rated R here in Australia. >.<
Cowboy Bebop - If you want more of the old and smooth anime which has good action!
Log Horizon - Like SAO except more character development (Well a bit more), fantasy world politics and world building!
Sword Art Online - Like Log Horizon except it is focused on mostly one character and his adventures in a world that can kill you ... also forced romance, bleh.
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JoJo's Bizarre Adventure[/sub]- It has it's serious moments, but has it's "THIS SHIT IS SO SILLY IT IS AWEEEEEESOME AND BAAADASSS" moments, good if you like that over the top stuff.
[sub]
Kill la Kill[/sub] - Speaking of over the top, this takes "Being serious" over the top. That should be enough ... might be too much comedy.
Baccano! - Baccano, a great gangster story with a good twist into the supernatural, sure it may have some comedy, but it is the comedy that fits right into the moment. Also it is a fun title to just say.
[Durarara!! - This anime ... man it has so many characters and conflicts that tie in, and it is done well!
[sub]
Getbackers[/sub] - Okay this fits into the old section like Bebop over there smoking it's cigs, GetBackers is a personal favourite of mine, two foolish partners who has badass powers that pretty much blow up the show.
Deadman Wonderland - Basically more bloody flesh, except more horror like and a prison setting with a super power twist.
Another - An anime final destination that isn't stupid at all, has horror and made me cringe in horror.
Fullmetal Alchemist: Brotherhood - If you like action, powers and two strong brothers which one is a
midget alchemist and one is a suit of armour, go watch it, highly recommend it!
Mirai Nikki - More horror except with supernatural phones and a bitchy protagonist with a stalking girlfriend. Fun. (Not bad for a early horror starter)
Higurashi no Naku Koro ni - Another horror, wow, basically Groundhog Day meets mystery and craziness.
Uncertain stuff
This is uncertain stuff because I haven't watched it.
Steins;Gate - Time travel mindfuckery.
Gunslinger Girl - Little girls trained in the art of guns ... doesn't sound too bad when you imagine a 13 year old shooting a FAMAS.
That is all I have, hopefully you shall find what you want in this or other people's posts. ^_^