I have never written a review before, nor do I plan to often in the future, but I felt that I ought to give it a shot here.
I'll leave out a lot of preliminary posturing and tell you straight up. As a long-time anime fan who has seen it all, from two-bit pulp series like Pokemon and Dragonball to art-house favorites like Akira and Princess Mononoke, I can say that Cowboy Bebop is, hands down, the finest anime ever produced for the small screen.
As with all creative works that are based on words (or a combination of words and images) the most important thing in a television series, be it anime or otherwise, is the writing. Needless to say, the writing in this series (Keiko Nobumoto receives the "Screenplay" credit, which I can only assume means that she was the head writer) is utterly fantastic and the translators have done a great job of conveying the real meaning and feel of the Japanese dialogue in English, rather than just translating word for word [Note: this applies to the subtitles, I NEVER watch dubbing; and yes, I do speak Japanese]. The individual episodic plots are well constructed and there is always the spectre of the overarching "uber-plot" mysteriously tantalizing you in the background. The characters are well-realized, interesting and three-dimensional, with the notable exception of Ed, the hacker, whose annoying presence is a result of the production company's desire to pander to a particular demographic of Japanese viewer. Fortunately, this character is not much used and the other three, Spike, Faye and Jet, are so cool and so interesting that the series could consist solely of the three of them sitting around, playing Mah Jongg and there would still be enough sexual tension and biting wit to keep it enthralling.
The show also has a great deal of variety in the flavor and character of its episodes, demonstrating the writers' versatility. Some installments are funny, others action-packed and others quietly introspective, or a combination thereof. The sci-fi (the anime takes place in a world that is both futuristic and retro) is very tight, and one of the show's real strengths is the realization of the world it takes place in. All the little details are in place and watching the show really can transport you.
Aside from the writing, the direction and overall look of Cowboy Bebop are beautiful and utterly cool. If you are at all a fan of jazz music or the jazz era in general, you'll love the color scheme, the inking and the lines. Director Shinichiro Watanabe does a fantastic job of creating the feel of coolness from days gone by while keeping you all the while, decidedly in the future. He plays with angles, rapid cuts, stills with voiceover, extreme close-ups and many other techniques, some of which can only be accomplished in an animated medium. He also makes great use of computer graphics, which not only helps bolster the futuristic feel, but gives Cowboy Bebop access to effects that few other animes have. All in all, the direction and production values, from the opening credits on, is totally top-drawer. It's not surprise that Cowboy Bebop was one of the more expensive anime series ever produced.
As for the music, what can I say? It features the compositions of perhaps the most-talented, versatile and interesting composer in Japanese show-business and certainly the greatest composer of music for animes alive today: Yoko Kanno. Her score to Cowboy Bebop takes all the best elements of jazz, pops, rock, classical and blues and wraps it all up in a score so wonderful that it is impossible that any TV series anywhere ever had a better one. If you're interested in the feel of the series, but don't want to commit to a DVD, try one of the OST Albums and I guarantee you'll pick up the DVD the next day.
I could go on, I could talk about the series itself, let slip some small details or give you a taste of the show's dynamic, but I think I've said enough. This is one of the few animes that I have ever seen that really is cool, fun and never, ever insults your intelligence. If more animes were like this our dates would perhaps not walk out on us upon the mention of our membership in the anime club. This is the epitome, the entelechy, the exegesis of all that is good about anime. Get it.
One final thing. ... likes to put what other people have bought as a recommendation underneath a product description, but this really does not provide any kind of meaningful help in most cases. Therefore, if you like(d) Cowboy Bebop I recommend the following:
1. Macross Plus: The Movie - Done by largely the same team as Bebop, utterly brilliant mecha series, the best of the Macross shows. (Also available as a 4 part mini-series)
2. Trigun - Fun anime series that may have been the inspiration for The Matrix. Only slightly less engrossing or cool as Bebop, it has some great characters and develops them to a great degree.
3. Gasaraki - Utterly fantastic political/fantasy/sci-fi drama. One of the best plots ever in an anime. A slow starter, but worth the wait. Also uses CGI, great production values.
4. Outlaw Star - A very poor man's Bebop. Nowhere near the production values or writing quality, but has it's moments and can be very funny. Fun if you don't expect too much.