A tricky subject, which I was forced to face once again today on the occasion of the announcement of the La Mulana port to Wii. Apparently, it will be given a higher-res graphical face lift, but as far as mechanics go it will remain the same (though I wouldn't be surprised if they found some way to tone down the difficulty...)
So what differentiates a remake from a port? Like I said, it's a bit tricky for games. For movies it's simple: there are no ports; every new version of an old film is automatically a remake.
I am really tired right now to think at all, so I am just going to throw this out there for the time being. In any case it's not a difficult issue, nor even an important one. But it's an issue nonetheless.
P.S. A solid example of a remake would have to be MGS: Twin Snakes on the GameCube. This is just an example to get people thinking.