Cowboy Bebop defines the modern era of anime. Set on the wild frontier of space, the bounty hunters of the spaceship Bebop are freelance heros, even if it isn't always willing. The characters are impecably developed, and you will find yourself identifying with them. The art is perfect, the likes of which are rarely seen, and show why you don't need actors for everything. The CG work is seemlessly added, rather than jumping out from the hand drawn work as it does in so many anime. And the score.
As for the action, yes, it is a part of it. But never is it gratuatous. Simply put, the Bebop's crew make the Nebacanezzar's look like school children. But it is thier story that pulls you in, not the action. It is THE classic tales of all cultures, told in a modern way. Rebirth, growth, learning, honor, death, these are the themes. The lesson... Well, that would be spoiling it, and not just becuase everyone sees something different from Jet, Spike, Faye, Ed and Ein.
I came for the art, I stayed for the story, and I went back for the music. Yoko Kana out did herself with the music of Bebop. From country to jazz to heavy metal to techno, it's all here.
Simply put, watch it. Start almost any where in the series, and just watch.