Story: Really what can I say that's not been said already. From the single episode stories to the overall one, Cowboy Bebop is an amazing anime. It is one of the select few that pulls off what it does well. One can really take away from each episode on their own and truly be entertained if seen whole. Episodes like Black Dog Serenade and Jupiter Jazz give such a great insight into the dramatic lives these characters lead while episodes like Pierrot le Fou and Brain Scratch can be really intense with endings that compels one to seriously contemplate on the presented subjects and characters. Not only does it deal with simple stories that are well done, but also with complex stories that most others are either afraid to attempt or too lazy to put the kind of work that's seen in Cowboy Bebop.
Animation: Classic old-school animation that so much adds to the overall style of the show.
Sound/Music: Classic anime sound effects with great fitting music. Tracks Green bird and You're Gonna Carry That Weight will be with me and my memory of this show for quite some time.
Characters: All the core characters, except Ed (I'll explain in a moment), are the kind of characters you can really relate to in a real and familiar way given that they each capture your attention and sympathy for the successes, failures, virtues, and flaws. Now, Ed for me was too silly a character that didn't seem to fit with the rest of the show. Really this is because I very much enjoy the mostly serious, but can be the funny-when-need-to characters it shows with Spike, Jet, and Faye. Core characters aside, you have amazing side characters like V. T., Fad, and Gren that while only seen sparingly or once, each add to the show in their own way.