I always try to beat either Earthbound or Mother 3 at least once a year. To me it's like reading a favorite novel to me. Also I love listening to the music.
I often play the first Mega Man Gameboy game on my 3DS. I used to play it on my old Gameboy back in the day, and it's one of the few Nintendo hard games that I could beat with some ease.
I also play Castlevania 2 Belmont's Revenge on a Gameboy emulator because some one did a rom hack, and made the Belmont sprite move faster. It seems more balanced now, and just a real fun game to play over and over again.
Speaking of Rom Hacks, some one created one for Zelda 2: the Adventure's of Link. The author of it wanted to make it more balanced, and increased the XP pick ups. I didn't really like the game back in the day, but I wanted to see if the changes made a difference. I ended playing over 4 hours, and didn't even notice. I'd say the changes made it a bit more engaging.