Cowboy Bebop is about a group of four bounty hunters called cowboys who hunt down criminals in outer space for money, quite the creative premise.
The main character is Spike who used to belong to a criminal syndicate. On the polar opposite extreme another character named Jet used to be a cop. Faye Valentine has been traveling across the galaxy and gambling a lot but also losing a lot to pay off some huge debts. Radical Edward is their computer genius. The unofficial fifth member of the group is Ein, who is their super smart dog and occasionally helps out with something.
The main villain in the series is Vicious and he’s actually a pretty good villain. There is a history between him and the main character, mostly to do with a woman. He uses a katana pretty well and has a bird that helps him in situations. He also is in charge of his own syndicate.
There is a lot of good action in this show with space ship battles, gun fights and fist fights. The conclusion fight scene with Spike taking down a syndicate is quite explosive.
Sometimes there is not a whole lot of humor, but some episodes such as the Mushroom Samba episode have a lot of humor. Radical Edward is the only comic relief character for the group and actually steals the show in my opinion with her quirkiness while the other three characters are all kind of serious and in my opinion flat, despite the backgrounds for each of them.
Faye Valentine is the main fan service character. Also, there is a romance between Spike and somebody he once was with named Julia. This is the main plot point for the series and drives the rivalry that goes on between Spike and Vicious.
The futuristic, almost cyber punk, outer space setting is pretty interesting and atmospheric.
The music is definitely one of the high lights of the show with each episode having a different style of music. The opening theme is classy and the ending theme is powerfully poignant and moody. There is even a heavy metal episode, which contrasts with the other more jazzy and bluesy episodes, but is nice to see for me, no grunge, though, which is also good to see, sorry grunge fans. Cowboy Bebop has a big reputation as being a classic anime and for the most part, I would agree with the people who say that.