I've long been a supporter of the rip-off over the remake. What I mean is that people should just rip-off movies and tweak them a bit so they seem different rather than remaking them outright. Die Hard was followed by a number of rip-offs: Die Hard on a bus (Speed), Die Hard on a boat (Under Siege), etc. A more recent example was the original The Fast and The Furious which was essentially Point Break with cars instead of surfboards; hijackings instead of bank heists. Flightplan was basically The Lady Vanishes on a plane instead of a train and with the disappearing person being the hero's son, not just a recent acquaintance.
In order for the rip-off to work, there needs to be enough difference so fans of your movie can plausibly deny that its a copy of another movie (Also, so the lawyers will be able to defend the film against any plagiarism charges). When a film fails to do that, it just looks like the filmmakers made a lousy remake. For instance, Disturbia was basically seen as a remake of Rear Window except by the writers who claimed that their work was wholly original. Another example is the trailer for Horseman, or what should probably be called "Four".