The recent remake of The Taking of Pelham 1-2-3 wasn't bad, in my opinion. It was just - like most remakes - not as good as the original. (The two most notable exceptions to this rule are Ocean's 11 and The Thomas Crown Affair. The remake of 3:10 to Yuma is in a dead heat with its original counterpart. Again, though, just my opinion.)
The original Pelham was free of the faux Hollywood "grittiness" and heavily-scored melodrama. The strength of the story comes from the realism of its characters - good and bad. The film manages to mix realistic drama and suspense with a wicked sense of humor. It's one of my favorite movies.
I think there are others who agree with me on this. Take a look at CappyNJ's clever editing of a updated trailer for the original film. (Pay particular attention to the "preview" notice. Clever, clever.)