Metroid: Zero Mission is the first thing that comes to mind for me. It's an example of a remake that's very different from the original so , but I'm of the opinion that the original is kind of hard to recommend to anyone who didn't grow up on it. ZM is just phenomenal and holds up perfectly.

I'll say Kirby Super Star Ultra for a remake that's nearly a straight upgrade over the original. The only real nitpick is that multiplayer is a little janky, SNES is obviously just a smoother experience for that.