OK, I didn't read all the comments so this was probably covered but: A) Constantine the movie is based off the comic series Hellraiser, which stars our friend John Constantine (the guy Reeves plays). He deals with Heaven and Hell and all its fun problems and angels and demons and stuff. It's pretty awesome.B) The real Constantine was the first Christian Roman Emperor. He has no impact on the Constantine of the movies or comics other than name. And the fact that Comic Constantine deals with the Christian system.
However, he does deal with other supernatural stuff (I haven't read much Hellraiser) on occasion, and even appeared in an issue of Sandman as his friend had Dream's sand. So yeah, Constantine of movie and comic =/= real Constantine. And I thought the movie was great, but then I haven't read a lot of Hellraiser so I can say nothing for faithfulness to the source. Reeves actually wasn't bad in this movie from what I remember, as Constantine is supposed to be an emotionless snarker. Oh, and the way he loses his lung cancer in the movie is pretty awesome (as was the devil) but different from the comics. Ok, ranted enough.