Well, for a lot of us, it's the first anime that we really watched or got interested in - which showed us the way to some fantastic stories in the genre.
It introduced some well-rounded, complex characters - all were more than they seemed. Over the course of the show they peeled back the veil of the past and showed what makes these people tick (to some extent) - what makes them the way they are.
It runs the gamut from the screamingly funny to the creepy to the touching to the incredibly sad.
There is enough mystery surrounding the main character, Spike, that leaves people wanting to know MORE. We have been given tantalizing clues as to his past, but we still don't know how he got to where he is now. Not really. The thread titled "The Official Spike Spiegel Fan Club" on this board has been taken over by discussions and speculations about what exactly happened with him and Vicious and Julia and why. How did he get his cybernetic eye? Was it REALLY an accident like he said? Why did Doohan give him the Swordfish? What were the circumstances of his even MEETING Doohan?
We LOVE the character, but there is so much about his life we Just Don't Know. He's cool, but what's running under the surface?
Faye is another one. We eventually DO find out why she is the way she is, but it ends before we find out how she processes what she learned about herself.
SO much is left open to interpretation. 12 years later and it's still being discussed and argued about. It's a classic and it's one that sticks with you - at least some of us it does. 
Also can't forget the music. This has the most amazing soundtrack of the most diverse collection of songs that are so worth listening to over and over again.
Obviously, not everyone has the same taste, or gets the same thing out of the show as others would. That's ok. For those who LOVE Cowboy Bebop, we know why we love it and we love to share it with others who may love it as much as we do. Or not. 
To clarify: I'm a chick, ok? And I'm a hugger. And I call people "honey." That's just how I talk (really). I live in the South (if you consider Florida to still be the "South") and it's what comes out of my mouth and hands on the keyboard."MATSUDA!!" Just about everybody - Death NoteBebop spoilers here: MrsSpooky's Cowboy Bebop BlogWATCH TIGER & BUNNY!