Death note and Cowboy Bebop are only series which are better on anime. Everything else is 1000x better as manga.

sword art online

you will thank me later

I'm no anime expert, but i'll recommend what i've liked so far.

Attack on Titan- I think this fits what you are looking for, lots of action and humans are pretty much at war with the titans.

Clannad- It's one of, if not, the most emotional anime I have seen so far (you might wanna get yourself a box of tissues, especially once you get to After Story). it is also pretty funny as well, but that depends on your taste in comedy. I can even go as far as saying that this anime changed the way I view life.

The Melancholy of Haruhi Suzumiya- Something about the supernatural in this anime made it really interesting. It does contain some fan service though, so I don't know what you might think of that. If you do decide to watch it, when you get to the endless eight arc just watch the first, second and last episode of it. I also recommend you watch the movie, It's really good, but you need to watch the series first to fully understand it.

Hajime no Ippo- This is a boxing anime, I don't really enjoy sports myself, but I really enjoyed this anime. It's not all 100% boxing, it also has its (pretty dirty) comedy and romance. The first season is pretty long at 70+ episodes, but it's well worth it.

These might not be your taste, but it doesn't hurt to try something you normally wouldn't.

Angel Beats!, Black Lagoon, Cowboy Bebop, Desert Punk, Elfen Lied, Fairy Tail, Gundam SEED, Hellsing, Linebarrels of Iron, Outlaw Star, RahXephon, Soul Eater, Tengen Toppa Gurren Lagann, Trigun, Witchblade. Just to get you started. A little warning about Fairy Tail, it's currently ongoing and approaching 200 episodes.

if you don't wanna list any specific preferences then just go to myanimelist.net

in the menu bar across the top go anime -> top anime

Those are arranged by user rankings. So basically the ones that users thought were the best.

However you listed Berserk so I will say that Hellsing Ultimate might be up your alley.

Also berserk I would almost call a psychological horror, a genre I personally detest especially when its from the Japanese, however Deadman Wonderland would also fit into that genre where it will disturb you rather than scare you.

Death note & Elfen Leid are excellent places to start.
Theyre both quite dark and very story driven.
Bleach is probably my favourite Anime series of all time but can be a little strange at times.

You like comedy/romance and slice-of-life?

 Yuri Yuri is really funny, I liked it quite a bit.  It's a girl's club anime, too.  Maybe School Rumble, it's absolutely hilarious.  You might like Nodame Cantabile and Skip Beat, which I mentioned before.  Yamato Nadeshiko is a good one, it's a comedy about a girl who thinks herself plain and ugly who is forced to live with four popular and handsome guys.  Kaichou wa Maid Sama is nice, too.  It's about a highly respected student who works at a maid cafe in secret, though of course the guy she thinks she hates finds out and uses that secret to get closer to her.

Sakurasou no Pet na Kanojo is about a high school student who moves into a dorm with a bunch of artist genius types, including a beautiful yet socially inept painter.  The Melancholy of Haruhi Suzumiya has good characters and an interesting plot.  Kimi ni Todoke is one of my favorites, though it might be a little slow paced for some people.  It follows a girl who is very nice and kind but who has been isolated because she looks like Sadako from The Ring.  It can be frustrating because she is so bad at communicating with people but that's also its charm.  Chuunibyou Demo Koi ga Shitai is a recent one that was pretty good.  It was about a girl that still pretended things like having magic powers and a boy who had to deal with her while trying to keep it a secret that he used to do the same thing the year before.

One of my very favorites is Chihayafuru.  I don't recommend it that much because it sounds boring, even though it's one of the best anime of the last several years.  It's about a girl who is "beautiful when she's sitting still" but is such a a goofy tomboy that she's called "wasted beauty".  She falls in love with a game called Kurata, where you take cards before your opponent.  I know that sounds boring but it's not.  It's extremely good.

Don't want to overwhelm you, so you should start off with these (because theres many, many great anime films or seasons that you haven't seen then).

Ninja Scroll
Gantz
Samurai Champloo
Trigun
Vampire Hunter D
Hellsing
Ergo Proxy
Full Metal Alchemist
Rin
Street Fighter 2

Awesome, thanks for the suggestions :)

argh...people: it´s Elfen Lied
not Leid

Lied means song in German and Leid is suffering/pain