This is my all time favorite anime. I have seen it many times, and own the series. However, I have not let my 10 and 12 year old watch it.
Pros: The main characters are well developed. Throughout the series you do grow to feel like you know them, and what they are thinking. The stories are good. The characters are intelligent, and have good humor. The female characters are free thinking and independent. The group takes in a homeless child and cares for her. When the characters do show emotional sides, they are believable and not too sappy. They are kind to animals, and have a pet dog. The soundtrack really great. The show is just highly entertaining. It is a guilty pleasure.
Cons (from a family perspective): Some of the things that give the characters depth, are also things that would make you not want to invite them home to dinner around your kids. Although there is never sex on the show, the characters are sexual. Spike makes some comments sometimes such as "I love a woman that can kick my ...." Faye wears a bright yellow next to nothing outfit that is barely kept together by a pair of suspenders. She has very large breasts that barely fit in her top, and are occasionally a focus of attention. From time to time there are gender identity issues that come up. The child character is named Ed, and often confused for a boy. A supporting character was transgender. The main characters also have some bad habits which include smoking, drinking, gambling, shouting, cussing, and fighting. There are firearms, and people do get hurt with them. There is occasionally blood, death, and a one suicide.
Wrap up: If you are a fan of anime and rated R action genre movies, you may (probably will) like Cowboy Bebop. If that genre doesn't really do it for you, than you will probably want to pass.
What other families should know
Too much violence
Too much sex
Too much swearing
Too much drinking/drugs/smoking