There are a handful of ways to look at this.
I think the guiding principal should be, generally speaking, to remake BAD movies that have great premises. It can range from basically phantom editing (Sunshine, sans the Sun Zombie, or circumcising the last 25 of A.I.) to total reworking. Michael Bay's The Island could very easily, and with little effort, be a brilliant story and film. It never explores the ideas it flirts with fully, and the bad science can be fixed without changing the story.
And it would be a waste to spend 50 million to remake Sunshine just to take out a zombie. You'd need an additional, stronger thematic reason. But when you start changing the themes and mood of Sunshine, you lose the parts that make Sunshine great. So movies like Sunshine and AI are in an un-remakeable position. Curse the filmmakers for not getting it right the first time and move on.
I'll tell you where I think coming close to direct remaking could work - Comedy. Dirty Work and Mystery Men are the prime examples. They're close to being perfect, but Dirty Work has some major flaws in pacing, editing and execution. A good director who isn't Bob Saget could have made gold of that film. It's a mean version of Ghostbusters, damnit. Shouldn't fail. And Mystery Men just suffers from being flat. It feels lifeless. It's so well written it overcomes the director. But what if it had a good director? But since a comedy is supposed to make you laugh, you can remake something almost shot for shot and I think the audience will forgive you. Provided its funny the second time around.
Reinterpreting can be fun, but it's mostly child's play IMO. I haven't really thought about it, but it seems taking an original story and transplanting it into a VERY different mold is interesting. I don't pretend to be a Bill Shakespeare expert, but I read Hamlet a couple times. And people tell me that Lion King is totes Hamlet n shit. And I can see where someone would say that. Good results.
To Teague's point on directors getting the same script - look no further than Fail Safe vs Dr. Strangelove. The scripts are almost identical and were released within spitting range of each other. In plotting and premise, no difference. Shows you how important interpretation is.
So yeah. I'd love to see The Island remade.