Cowboy Bebop is an anime series written by Keiko Nobumoto and directed by Shinichirō Watanabe. The series follows the adventures of the crew of the spaceship Bebop as they try to make a living hunting bounties. As you might expect, they are bounty hunters, known in-universe as cowboys. Each episode, called a session, has a distinct musical theme and a title that reflects the theme. (This writer highly recommends the series' soundtracks.)
The main character of the show, Spike is tall and lanky with a penchant for cigarettes and getting himself into trouble. He has a smart mouth and a lackadaisical attitude, which tend to combine in unfortunate ways. However, he is just as good at getting out of trouble as he is at getting into it, thanks to his graceful fighting style and the fact that his friends seem to like him for some reason.
Jet is the owner of the Bebop. He is a powerful man with a cybernetic arm to remind him what happens when people rush into things without thinking them through. As a result, he is the more pragmatic of the Bebop's crew, usually the first to point out the impracticality of Spike's schemes, but always aware of how desperately broke and hungry they are.
The first of three crew members to be adopted over the course of the show, Ein is a Welsh Corgi and a "data dog." What this means is never exactly explained, but it is clear that Ein is very intelligent. Unfortunately, the human crew members seem not to notice most of the time.
Faye wakes up from a 54-year period in cryogenic stasis with no memories of her past and a heavy debt to pay. Her first encounter with the crew of the Bebop is as a rival gambler to Spike, who sees through her cheating and makes off with the winnings. (Of course, his luck being what it is, he doesn't get to keep them.) As she and the Bebop keep crossing paths, the rivals eventually come to an uneasy truce, and Faye becomes part of the team.
Ed is a young girl often mistaken for a young boy due to her androgynous appearance. She is an eccentric computer genius and hacker who seems to speak a language all of her own. She spends the most time with Ein.
Spike's former partner in the Red Dragon Crime Syndicate. As his name suggests, Vicious is not a nice person. He believes in killing his way to the top and recurs as an antagonist in the series.
The mysterious woman in Spike's past, and one of his primary motivating forces. However, she appears only in Spike's flashbacks until the end of the series.