I am currently watching Tiger & Bunny. Its been a while since I enjoyed watching an anime this much.

Dunno if people have already said these...

Ergo Proxy
Texhnolyze
Death Note
Serial Experiments Lain

Evangelion goes without saying, whether you love it or hate it you need to have 'experienced' it at least once if you like anime, just so that you can say you saw it.

This and Akira. Do it.

A great show from the Winter season was Puella Magi Madoka Magica, a VERY dark take on "Magical Girl" shows. It's not licensed for distribution outside Japan yet, but AFAIK talks are ongoing. And fan-subtitles are not exactly hard to find; this show was EXTREMELY popular.

Another personal favorite of mine is Bakemonogatari, a slice-of-life show about a boy who helps various girls with supernatural problems. Again, not licensed outside Japan, but AFAIK talks are in progress.

Hell, anything involving Studio SHAFT and its' head Shinbo Akiyuki (the aforementioned two series included) is awesome in my book.

Good news at anime expo 2011 from aniplex:

http://unobtainium13.com/2011/07/02/aniplex-usa-has-licensed-puella-magi-madoka-magica/

I liked CB and GITS a lot (especially Stand-Alone Complex), so you might like an offbeat non-SF series I enjoyed, XXXholic. It has a unique take on the supernatural, very atmospheric like a good spoken ghost story. The male lead is whiny but in a quirky way. The chemistry between all the characters is very good. Give it a few shows to get a sense of the rhythm.

Noein is an intriguing SF series mixing quantum probability with coming of age, nostalgia, and lots of stylized and fluid fighting scenes. It's a lot more thoughtful than most.

Satoshi Kon did several very original movies before dying way too young.
Most boring "edgy" show I ever saw.

WTF I can't believe no one's mentioned my two all time favorites:

GTO and Hajime no Ippo. That and Initial D.

That is all.

[url=http://myanimelist.net/anime/44/Rurouni_Kenshin:_Tsuiokuhen] The Ruroni Kenshin 4 episode OVA [/url]
Watch it here

Also, Baccano!
Do you have Netflix? Because you can watch it online dubbed there. YOU MUST WATCH IT DUBBED. If no netflix, watch it here.

As most people have said, watch Black Lagoon

Watch it here

If your into samurai action movies with really superb animation and good music, I'd recommend Sword of The Stranger

Watch it here

There are three mech shows that I REALLY like. Mostly because they're not really about mechs. Either way:

Eureka 7 (watch it here )

here )

Tengen Toppa Gurren Lagann (watch here )

This isn't an action anime but you owe it to yourself to watch Naoki Urasawa's Monster.
It's a dark, gritty, mystery-style anime that doesn't have any of the three things you said you didn't want.
You should probably watch the first few episodes and if the story hasn't peaked your interest by then it probably won't.

I'm not really a big Anime fan, but i seem to have the same standards as you ;) a few that i only saw mentioned once (i just skimmed the threats) that i really liked were

Elfin Leid and Monster

Kino’s Journey. A young girl travels from country to country staying in each place for three days. Also it has a talking motorcycle.


When you're done with Baccano! you might want to take a look at Durarara!!

Its not for everybody. I would also say that it does try to be to edgy for its own good. Its far from my favorite show as well. Still, I think its pretty good. There is way more character development than the vast majority of anime out there, and I would say that's a big plus. I didn't pick it based on my own feelings though. The OP wanted gritty and action packed. Gantz is gritty and action packed. I felt the need to push Ergo Proxy on him, but all of my other suggestions are things I thought he might like based on his criteria, not MY favorite things to watch.

Tracking information shows that Rideback will show up in my mailbox tomorrow. Tomorrow also happens to be my birthday. True story. Im all stoked up about it.

If you want something different but really really great, watch the animes of Masaaki Yuasa :
Cat Soup
Mind Game
Kemonozume
Kaiba
The Tatami Galaxy

And some really other great and original animes :
Atama Yama
Inaka Isha
The Diary of Tortov Roddle
La Maison en Petits Cubes
Tenshi No Tamago
Glassy Ocean

And from the already mentioned animes, Perfect Blue, Serial Experiments Lain, Texhnolyze, Kino No Tabi and Monster are really nice! and Mushishi too! And so many other animes...