This is my favorite anime of all time. It told a complete story from start to end and the quality of the animation and the voice talent was near perfect. I tell people that if you want to give anime a try or even if you don't get the fandom or why some people really love it, then check out Cowboy Bebop. I think it's the best series to convince people that a great story can be told through animation.
I totally agree with you. I especially love the characters and atmophere. It's all very convincing, with flaws and imperfections. In a lot of animes, the characters are poorly written, but in Cowboy Bebop, it's very believable that they could actually exist!