Cowboy Bebop excelled in mood, style, atmosphere, but ultimately, for me, lacked in story. Some of the stories did keep me interested, especially looking into the pasts of our characters, or some of the particularly weird ones, but often I was bored. Well, one difference between me and some of the rest of the world - I'm not a big fan of action sequences, shoot-em-ups, or cool posturing, although cool posturing can be, well, cool, at the very least.
The shining point for this series is the music. It was consistently a joy to hear what awesome or unusual musical track was running in the background.
The next shining point was the atmosphere - the world. Somewhat post-apocalyptic future, a gritty world. Also, the mix of genres, from the space future to the old west to jazz to blaxploitation to all things pulp.
The next shining point was the characters. I liked Spike and Jet, but I really kinda liked Faye because she was more interesting, and I loved Edward for being endlessly eccentric, not to mention adorable and lovable.
While the stories often had me bored, I did have a great appreciation for the method of storytelling. They never took the easy route, choosing instead to engage your capacity to put together abstract visions into a concrete story.
I guess I was a little disappointed in the ending, having read so much about it. The reason I decided to watch Cowboy Bebop was there was mention at Wikipedia that it featured the themes of existentialism and ennui. That truly appealed to me, but in the end I didn't really feel I'd had any kind of transcendent experience with existentialism, despite a certain malaise of not knowing where you belong in the world, who you belong with, and being faced with the tragedy of death. One reviewer here at anime planet stated that the last two episodes were the best ones that tied the whole series together, but as for me I preferred many of the episodes from say 17 to 24.
So I definitely recommend this anime, but especially to people who enjoy ninja/crime/western/space shoot-em-ups with too-cool-for-you heroes, and also to those who enjoy imaginative plots and great music.