It depends on the game and the nature of the remake.
Game mechanics cannot be protected by copyright, trademark, or patent. You can freely copy the mechanics of any game you want, as the basis of a new game. (This is why there are so many clones of things like Scrabble and Tetris out there, Snake clones are a common programming exercise, and many computer RPGs have mechanics that are strongly reminiscent of those from Dungeons & Dragons.)
However, the creative aspects of the game are protected by copyright. You'll need entirely new artwork, created in a way that doesn't make it a derivative work of the original (eg. by giving the artist bare-bones descriptions of what you need). Any re-use of the original storyline is entirely out: I can't picture a way of using it as the basis for your new game that doesn't create a derivative work.
Additionally, the game's name is almost certainly protected by trademark, either registered or common-law.