How could I forget...

Paranoia Agent. Totally worth the cost of admission. Easily one of the most engrossing anime series I have ever watched, very deep stuff if you like deep stuff.

Both Full Metal Alchemists animes are very good but full of the things you dislike about anime. lol But are still great

Samuria Champloo is a good anime made by the same peoiple who made cowboy bebop but instead of space jazzy western it is a medieval hip hop samurai story.

Also, the bonus is easy. The anime Monster is great and isn't any of those things.

I also love Vision of Escaflowne (the series not the movie) Great art work, well written, silly concepts but done so well.

And even thouugh I'm not a fan of it, you may want to try Trigun, it is a sci fi western like Cowboy Bebop but with a bad ass dude who doesn't want to kill like Trinity Blood.

I realize some of the ones I choose others have and there are some other great ones others mentioned such as Baccano, Paranoia Agent, Big O, etc.

I watched PlanetES recently which was a really good hard science fiction show, but there wasn't much action. Something more along your lines might be Gundam SEED.

Maybe these:

Le Chevalier D'Eon
Gasaraki
Boogiepop Phantom