List of Nintendo made remakes:

The Legend of Zelda: Link's Awakening DX
The Legend of Zelda: A Link to the Past GBA
Super Mario All Stars SNES
Tetris/Dr. Mario SNES
Metroid Zero Mission
Legend of Zelda BS (Japan only)
Pokemon Leaf Green/Fire Red

Quote from Eiji Aonuma cited on Wikipedia, "Ocarina of Time was the first title I worked on, and I was continuously tackling challenges every day during its development, so I think this is the title I feel I impacted the most. I believe that experience made me what I am now. I always think about what we couldn't do and what didn't work well in the previous game when we start a new title, but there's no game that I would want to actually change as such. I have to say though, the first Zelda game that I played and felt potential in was A Link to the Past. I'm actually very interested in what it would be like if we remade that title as a 3D game."