Super Mario Advance 3: Yoshi's Island and Super Mario Advance 2: Super Mario World were my first Nintendo Games, and they're both still in my top ten favorite games of all time.
The first Nintendo game that I ever played was Super Mario World on the SNES. I remember that my uncle gave me his old SNES and the game and I played it for countless hours as a kid. I grew up in a relatively poor family so we didn't get many more games for years. It was so much fun finding new secret areas and the like (especially in the time where we didn't have the internet to look them up so easily) and even still I enjoy coming back and trying to speed run it now and again. I've still got the cartridge and the SNES both in working order.