The whole feeling I get from Cowboy Bebop is just amazing, I dunno what it is about it but it might be the way it approaches life in the future so casually and normally.
Strange Anecdote Ahead:
Years and years ago I found a Phantasy Star Online video on youtube, which had music from Daft Punk in it. It was the first time I'd ever heard Daft Punk and it stood out to me so much I began to listen to them more and more, and eventually told a friend about them (this would have been roughly 2007-ish). He too enjoyed them and it turned out that his father who was, and still is, really into collecting Vinyl (especially funk vinyl) had their Discovery album on vinyl. I remember being over at his house and having it going full blast, simply because we both loved the shit out of it (and to this day we both still do). I eventually watched the anime styled film that Daft Punk directed 'Interstellar 5555', which has no voice acting, instead using Daft Punk's music as all the sound it in, and it reminded me of that initial Phantasy Star Online video I saw because the whole aesthetics of both the film and the game seemed so connected, despite not being connected at all.
Both PSO and Daft Punk/Interstellar 5555 have been pretty constant ideals for my personal taste when it comes to anything sci-fi related, and then after everyone and their mum talked about how good Cowboy Bebop was, last year I thought I'd finally sit down and give it a watch.
Something about it just clicked, and slotted in perfectly to what I loved about PSO and Interstellar because they all seemed to have similar traits, and it reminded me so much of how much I loved them. The jazz soundtrack was similar enough to Daft Punk's music and the visuals were similar enough to PSO to make me love it, albeit not until I had finished the series.
What Raz says about nothing really happening is something I can certainly agree with though, the story involving Julia and Vicious especially confused me. Looking back on it now I find it strange how there were episodes setting the story revolving Spike's past with Julia and Vicious, but as I recall they were scattered through the series. I guess it makes for more realistic story development, but the fact that it wasn't in one large arc at the end (a la Clannad, the last show I watched seriously before Bebop) made me seriously worried that I had missed out some really important plot element about the characters.
Edit:
Got to looking around at Bebop stuff after posting this, someone stitched together the panoramic shots in it and it looks fucking amazing. This picture from episode 10 is exactly what I mean by the feel of PSO, Bebop and Interstellar.