Let me tell you why, in no particular order;
It looks lovely. It's stylized, and looks convincing gritty without being gross. I really appreciate that the women look attractive without having gigantic boobs or particularly revealing clothes.
Hardly anyone dies. The show makes you feel for the characters, and makes you want even the most obscure side character to be okay. It doesn't fall into that trap that a lot of anime does, where the only major emotional experience is caused through death, and not plot development. The show is really mature with death during the climax, too.
J's English voice actor does an amazing job. Bob Papenbrook creates the perfect mix of monotone and emotion, so that you can tell J is different, but is still easy to become attached to.
All of the characters are multi-layered and enjoyable. Even though I love Yu Yu Hakusho, whenever they have Hiei do something silly it feels really OOC and awkward. Yet when Boma, the Heat Guy J equivalent of Hiei, does something silly it never strays too far from his personality. Him holding that stuffed bunny for Monica seemed exactly like something he should do. Every character gets mad, sad, happy, etc., without any one-emotion stereotype.
It's adorable. All the characters, even the ones that start out unlikable, end up being good-at-heart and just wanting to live life. Clair and Dice's frenemy relationship is odd yet super adorable. And J's out-of-the-blue life quotes are well-timed and pleasant. J manages to be intimidating and a big teddy bear at the same time.
It's hilarious. Especially towards the end, even though the show still maintains plenty of action and seriousness. I crack up every time I see Parsley in a room, and that guy serving food in the middle of the war zone has Ultimate Swag. I also enjoy how the creator of the show is practically afraid to animate any Boma action scenes. (that is a minor downfall of the show: it recycles animation sequences and has some abrupt action scenes, but that's not too upsetting)
The ending is very satisfying. I would have liked Dice to stay (not quite sure why he even left, but I guess he craved adventure), and would have liked to see what everyone else did with their lives, but I still felt very fulfilled watching it.
It's full of hot guys (this is more of a personal preference). Even J is super hot. He may not be straight-up handsome, but he's a muscly guy that I find attractive. It may be more his personality, though, because he's a Real Man just like Yu Yu Hakusho's Kuwabara. I love his eyes, as well, and he's such a snappy dresser. Boma is also super hot, with or without his holographic head present (he doesn't count as a Furry because he was not born that way, it's only his head that looks that way, and he sees himself as human).
Everyone has really nice character designs. Everyone except for Boma wears realistic, practical clothing, and not some Final Fantasy dress made out of belts… even the stranger outfits can be excused because, hey, have you seen the outfits people wear in Transmetropolitan? That's what you get for living in a city in the future.
I could probably find more reasons, but I think this is a good start. I don't think I've ever cried over an anime, but I almost cried happy tears at the ending and I was really worried for J a few times. This show is currently tied with Yu Yu Hakusho for my Favorite Anime Ever. It could possibly even surpass it if I wasn't so stubborn about nostalgia.