The Man With X-Ray Eyes is definitely a classic, and could stand an intelligent remake. The original was by Roger Corman, who went for a basic script, but the possibilities are endless. For example:
He could see the microscopic, as well as the telescopic. He might look at the ocean and see its bottom.
And in the original, he thought that in the vastness of space he saw something like God. However, that could be rewritten as the devil, and when he looks at it, it looks back, and starts coming in the direction of Earth.
So many possibilities.