Keanu Reeves plays a man in a black trench coat chosen by fate to uncover the shocking truth that Earth is not as we believe it to be, but merely a mundane illusion hiding an army of insidious and overwhelming enemies. So, basically, it's The Matrix with crosses.
In the comic (called Hellblazer), John Constantine is a foul-mouthed con man who exploits the forces of both heaven and hell, using dirty tactics and minimal supernatural abilities to foil chumps of all shapes and sizes.
In the movie, he's a repentant Catholic destroying demons to save the soul of a little girl and earn his way into heaven. Keanu apparently requires all of his characters to fulfill the "savior" role to a spectacular degree. We're surprised Bill & Ted's Excellent Adventure didn't contain a scene where Ted travels to Jesus' time and, in some kind of wacky mix up, dies for all our sins.
Like the comic, the movie revolves around Constantine trying to get demons to cure his lung cancer. But, after he succeeds in the movie, John quits smoking. Come on! You've just annoyed Satan into magically taking away your lung cancer and you're quitting smoking?! Your lungs are magic! If anything, you should start smoking four or five cigarettes at a time with the filters ripped off and the tips dipped in ether.
Why did they change it?
Say what you want about comics, but they've got Hollywood beat when it comes to the whole moral-ambiguity thing. Keanu's Constantine has just enough token flaws to be cool, and, in true Hollywood fashion, loses them all by the time the movie ends.
Strangely, though, losing everything that was fun about the comic book character wasn't enough. They also changed a bunch of small, arbitrary stuff, like the pronunciation of his name (in the movie rhymes with "tangerine" instead of "turpentine"), made him American instead of British, and did very little to make Reeves look like Sting, who was the original inspiration for the character. If that much needed changed, why adapt it at all?
Did it work?
Alan Moore, Constantine's creator, hated the movie so much he asked his name to not be put in the credits. Of course, he's done that with every movie made of his work, and at some point you have to wonder if he's just being a drama queen. The guy does wear a good number of oversized rings, and sports a beard large enough to house a family of raccoons. He clearly likes to be looked at.
That still doesn't mean Constantine didn't suck.
Jim Carrey discovers a magical mask that allows his face to become slightly more elastic than it already is, and uses this ability to reenact as many moments from old Tex Avery cartoons as is humanly possible within a two-hour period.
In the comics, the green-headed character is not, in fact, named The Mask. His name is Big Head, and rather than humiliating villains by pantsing them in front of their henchman, he mercilessly kills anyone that the mask's wearer dislikes and indulges in his every id-driven whim. The main character (Stanley Ipkiss) kills some people who don't deserve it, is verbally abusive to his girlfriend, then gets shot in the back and killed.
The cop who's after Ipkiss (Lt. Kellaway) eventually puts on the mask himself and goes on a murderous rampage, nearly kills his partner and flees in horrified shame.
Stanley becomes a lovable loser who pursues the woman of his dreams and ultimately uses the powers of The Mask to thwart an organized crime boss. Wackiness ensues.
Lt. Kellaway turns into your basic gruff, overweight policeman doing a lot of exasperated takes at the ends of scenes and yelling at his dim-witted partner. The film gracefully adapts Kellaway's violent rampage into a scene where the Mask yells "AHOOGA!," lifts Kellaway's shirt and blows on his belly.
Why did they change it?
As with Judge Dredd, the little-known comic became a vehicle for a Hollywood star who completely overpowered it. Carrey hadn't moved into the brooding, dramatic phase of his career yet and used The Mask as an excuse to play a zanier Ace Ventura.
Did it work?
In the comics the contrast between a cartoon character and realistic acts of mayhem is a little easier to swallow since, well, everyone is a cartoon character. On film, you kind of have to pick: Either your character is a murdering badass, or a shape-changing wiseacre. They went with the latter and wound up with one of Carrey's more entertaining early films.
Fans of the comic were no doubt outraged, but any attempt to play it straight could have resulted in the same off-putting combination of CGI and pathos that Hulk turned out to be.