Cowboy Bebop is the best anime ever. I'm 21, don't tend to be fanboyish, and have seen plenty of others. And it's the best anime ever.
What other anime features a mix of the best choreographed/energetic/ kick-ass fighting scenes - hand-to-hand, hong-kong gun fights and air-space battle?
An unbelievable mix of comic, tragic, violent and fairy tale style episodes...
An incredible sound track - Yoko Kanno is a genius that can do memorable and emotional jazz, blues, classical, fantasy-style, j-pop and even heavy metal. I wouldn't even consider buying the soundtrack to any other anime.
It quite literally oozes "cool" - characters (Spike is probably the coolest - not awsomest, but stylishly coolest) music, action and narrative.
Hell, it's the only show that has both a "cute animal" character and a "cute annoying kid" character that I don't wish a horrible death upon. And if that doesn't convince you, then nothing will.
10/10