I haven't read the Hellblazer comic books by DC/Vertigo, so I do not know much about the John Constantine character, or how the show deviates from the comic books.
However, without background knowledge, this is one excellent movie, with great characterization of biblical characters like Archangel Gabriel, Balthazar and even Lucifer himself, plot and subplots, special effects and music. The movie starts literally with a bang, and it never lets up after that with its even pacing.
Keanu Reeves has proved that once again he is master. To his detractors, I'd say hold your horses, watch this show, and chances are you'll be a fan convert. Rachel Weisz, wow.
Hell has never looked as good (!) as what's shown in this movie. The effects are world class, and brings forth to glory and life, the demons and damned creatures from hell.
The Constantine Theme provides the noir, a dash of suave and attitude to the movie and when it's on, you just know something awesome's about to happen.
Stay till the end of the movie, it'll show you the aftermath of one of the characters.