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Akagi. A gambling anime about Majong. Heavy in suspense and badassery.
Afro Samurai/Afro Samurai: Resurrection. Action anime, not much story. Tons of style. Great english version with big name voices. (Samuel L. Jackson plays the main character.)
Baccano! One of my personal favorites. Pulp fiction set in 1930's about immortals and murder mystery. Great english version.
Beck: Mongolian Chop Squad. About a band and it's rise to fame. Fantastic series that even non-anime fans can enjoy.
The Big O. Mecha series with steampunk mechs and great characters.
Black Lagoon. American influenced gunslinger series. Good english dub.
Cowboy Bebop. This series is perfect. Watch the english version.
Detroit Metal City. Comedy series about a Japanese kid who likes trendy Swedish pop music, but ends up as the lead singer in a death metal bad. Rape jokes follow.
Golgo 13. Badass assassin. Insane manliness and sweet gunplay here.
GunXSword. Average story, but great characters and action. Not much to say about it.
Gungrave. Based on the video game series, it tells the backstory as well as the main storyline of the games. Start from episode 2 for max experience. If you like mafia stories, go for this.
Kaiji. Just like Akagi, it's a suspense series about Gambling. From the same creator.
Le Chevalier D'eon. Deep storyline, great rapier fight scenes,beautiful backgrounds of a early France, and a fantastic story. An underrated masterpiece.
Mobile Fighter G Gundam. Watch this in english. Unlike most gundams, about war, this is a one on one fight series with ridiculously over the top action, and racial stereotypes that can't help but be hilarious. (Canada has the Lumber Gundam, America has a boxing/Football player gundam, etc.)
Noein. Heavy on story, Noein is a story of multiple dimensions/timespaces and quantum physics. Avoid if you hate series that will make you think.
Read or Die. Go for the movie/OVA series, it's about a secret agent who can control paper to fight. Pretty good plot, great action.
One Outs: Baseball anime, but about psychological attacks over boring typical sports shit.
Samurai Champloo. Samurai action, heavy on combat. Same creator as Cowboy Bebop.
Scryed. Over the top action. Nothing more. This show is one big fight.
Tengen Toppa Gurren Lagann. I don't need to say anything, as I assume many people already brought it up. Personal favorite series.
Top wo Nerae!/Gunbuster. Oldschool series, Gurren Lagann draws heavy influence from it.
Top wo Nerae! 2/Diebuster. Even more over the top, and inspired Gurren Lagann a lot more than Gunbuster.
Not such a good list if you're looking for typical DragonBall Z styled stuff like Bleach, Naruto, One Piece, etc, but if you want some good series, try these.