Cowboy Bebop follows the adventures of a group of space bounty hunters. The series takes place in the not too distant future, mankind has created colonies on several other planets in the solar system using jump gates that give us faster than light travel. A consequence of this technology is that the earth gate was destroyed and took a large chunk out of the moon. The resulting space debris that falls to earth often, has made earth a very hazardous place to live.
As a musician and anime fan I particularity enjoy Cowboy Bebop. The reason for this is because each episode is composed around a musical theme. Jazz is the primary type of music, but certain episodes use other styles. The pace of the episode, the action and the type of story are all keyed into the music.
The principal characters have sordid pasts, and interesting personalities. The interaction between them is really the focal point of the series. The other main themes through the series are their almost constant lack of money, and their past coming back to cause trouble.
An ex-cop, an ex-yakuza hitter, a hot chick with a gambling problem, and a young girl with a boys name longer than your arm. Those are your main characters, and they are every bit as fun to watch as they sound. The most rag-tag bunch of bounty hunters to ever take the title space cowboy.
The series also has some very good side characters. Each episode generally has a bounty they are after; each a distinct character rather than just generic baddy 'number whatever', and / or a guest character that helps drive the story. The willingness to give real depth to side characters is one of the things that makes the series so very good.
I rank Cowboy Bebop as one of my top 5 all time favorite Anime shows. If you have not ever watched it, I highly recommend it. Be forewarned it does have some pretty violent action, and occasionally adult oriented humor.