For reasons more fully explained in my posting for Ghost In The Shell: Stand Alone Complex. So I can be brief hereĀ
First, Cowboy Bebop is an anime series that actually made me care for the characters and want to learn more about them. Be assured that is one extraordinarily rare occurrence on TV, at least for me.
Next, several story arcs were at first hinted at, then truly converged and were resolved by series' end. (You might not like the resolution, but a resolution it well and truly is.) In fact the series became more interesting as it progressed. (The movie is a careful thematic side step, neither adds nor detracts.) Excellent voice acting and characterization in both Japanese and the dubbed English. Exceptional music that introduced me to the works of one Kanno Yoko and The Seatbelts.
And as with GITS:SAC, action, obligatory gore (albeit animated), some expletives and "cheesecake" (ditto), but all tempered with a captivating and truly surprising allotment of characterization, dialogue, insight, wit, and "breathing time."
Time well spent, and the best introduction I can think of to the genre.