I am pretty picky when it comes to anime. I tend to like it gritty and action oriented. I am currently watching D. Grayman which is meh. I don't like Naruto, Inu Yasha, Bleach and such.
I loved:
Cowboy Bebop
Appleseed
Ghost in the Shell
Hellsing

Enjoyed:
Claymore
Trinity Blood
And more that I can't remember yet.

A prize for someone who can find one that I like and doesn't have:
Long intro/credits with still shots and a lead vocal heavy song
Overly done whiny male anime archtype
Over done flipping out
I believe I just outlined the three pillars of anime so good luck.

EDIT: And mention where the best place to watch it is. Thanks!

My Favs:
- Record of Lodoss War
- Bubblegum Crisis
- Akira

Baccano!

Black Lagoon.

I thought Sailor Moon, DBZ, and Pokemon went without saying since everyone has seen them ;)

Hm, I think I have seen a little of Rin I think. I will have to check...

Texhnolyze.

Eden of the East, is really good kind of spy-esk in near future:

Kannagi: Crazy Shrine Maidens, is a nice slice of life with magic

Samurai Champloo, is just good

Death Note and Paranoia Agent are two of the best out there, IMO. (Okay, okay, so DN has a lot of flipping out and the obligatory long intro sequence with a rock-metal soundtrack, but it really is worth watchin.)

Macross Plus and Macross Zero are pretty good too.

My vote goes on Elven Lied.

I concur. If you enjoyed Cowboy Bebop, you'll probably enjoy Samurai Champloo. Made by the same creators and similarly built, though instead of jazz and space it uses rap/hip-hop and feudal japan.

Golgo 13 maybe? Its genre should be "episodes of people explaining why they want something shot and then the something gets shot, in the face". I always skipped the intro so I don't know about it, but you don't see Duke Togo whining.

I second ceemdee's suggestion of Black Lagoon.

I assume your mention of Ghost in the Shell includes the Stand Alone Complexes and whatnot, if not, watch those (the 1st GIG is my favorite anime series/season of all time ever ever).

I've only watched a few episodes thus far (even though I have it all on dvd), but Ergo Proxy seems kind of good (but I got so busy that I had to stop watching it and I never remembered to get back to it). The opening is good enough that I actually didn't skip it.

Berserk is great. I've watched it many times (skipping the last few episodes). The opening/ending songs are legendary, but not in a serious way.

IMO Vampire Hunter D: Bloodlust is a great movie (but sadly it comes with occasional strobo lights).

I think the best place to watch 'em is the living room, if you have one ;)
Excluding Golgo 13, every one of them can/could be bought relatively cheaply from Anttila. Probably doesn't help you much, though

This one is probably your best bet.

If you don't mind some really old stuff that is only available in subs, Armored Trooper VOTOMS is as gritty and action packed a it gets.

Some other more modern stuff you might like would be:
Gantz
Gungrave
Speed Grapher
Blue Gender

You might also consider Witch Hunter Robin. Its not quite what I would call action packed, but judging from the things you listed as liking, its at least worth watching a trailer or something.

I also have to mention Ergo Proxy. Its my favorite, you see. My avatar is from this show. Its got a dark an moody type of atmosphere, but its not action packed. When there is action, its great. Its also quick, and not in every episode.

Edit:
Oh, I forgot Karas. You would probably like Karas

Pokemon. Great GBC games as well.

i can recommend samurai champloo too, it's not bad at all.

And as always i won't miss the chance to mention FLCL if you haven't seen it, go watch it right now.