It's already been done. It's called "True Blood"Grach said:The only way to remake Twilight and do it right is taking the basic premise (girl falls in love with a vampire in modern times) and just integrate good characters and a good story, eliminating the awful implications of the series.
You can certainly argue to about the quality of the series, but I liked it pretty well (or as much of it as I've seen, I've only watched through the first three seasons so far, I think). Certainly it is better than whatever that Twilight stuff is (I refuse to call it "vampire". Those are NOT vampires).
Let's see: My vote would go to "Blade Runner". The old Harrison Ford version is of course a classic, and you don't want to mess with that, but on the other hand, if it was done well, it could be a good time.