Cowboy Bebop is one of those anomalies that transcended the norm; it wasn't popular in Japan initially but was a big hit in the Western world, it paid alot of homage towards its' Western influence & it was slightly more realistically mature.
When I say "realistically mature", what do I mean? We've had mature themed anime in the past (Macross, Ghost In The Shell, Akira) but Cowboy Bebop was one of the first, to me, that was set grounded in real life. Even with the fancy new toys and futuristic setting, it was essentially a love triangle that has gone wrong.
It was Spike, Vicious, & Julia show and everyone was just tagging along for the ride.
I'm pretty sure most of the points, good or bad, I can discuss have been pointed beforehand, and much more eloquently than I would so I would just like to leave some parting words.
If you like space westerns, space operas, cyberpunk, great action scenes, awesome dogfights or a really mature premise; then this is the anime for you. If not, check it out anyways. :)