The TNT bowdlerized version doesn't suck as much as you might expect, but that's a bit damning with faint praise.
The part of the movie that appeals to me isn't so much the over-the-top Tarantino violence, although I'd be lieing to say I don't enjoy it, its the cinematography he stole for the film. The end of the film is my favorite: he manages to capture the feeling of Anime Japan, and the style I love, with out the annoying shit so many of the actual anime directors end up using. The best example is the arrival sequence in Tokyo.
From there on out its pure gravy.
Incidentally this is the major complaint I've heard about the movie. Perhaps its my love of good fan-fiction that makes this movie appeal to me so much. Of course part of the appeal is then going out and finding the sources, to watch the original and see how it compares to the retelling.
Edit to Add: Dr. Paws gives it a paw of approval for a movie to sleep through curled up next to me.