+1 to Cowboy Bebop!!!
That is one of the best Anime series of all time, hands down! I have it on DVD, I doubt I will upgrade to BD. I love the animantion, action, and of course the jazz beats!
If you like that, then there are a few others to mention that you should look into:
*Samurai Champloo (same team that did Cowboy Bebop): It's another epic series. Great, but not quite as good as CB, and what a surprise ending! Also, the soundtrack more focused on hip-hop and turntablist beats rather than jazz.
*Lupin the 3rd: Yeah, it's old anime so the animation is dated. But the storyline and the little jazz beats are there. When you watch it, you will realize that this is absolutely the roots of CB. Completely different story and characters, but very similar in style.
*Afro Samurai: It's OK, stars Samuel L Jackson. Decent storyline, decent animantion and beats. Mostly, I guess it's kind of the American attempt at anime. It's reasonably good, but not great in my opinion.
On a side note, I see Appleseed Alpha is now on BD. Appleseed has always been at the forefront of the animation tech.