For me, the original "The Legend of Zelda", is the game I replay the most and never tire of. I've been playing it since 1989 from start to finish on NES, GameCube (Collector's Edition), Wii (Virtual Console), 3DS (Virtual Console), and Wii U (Virtual Console).
Arcade type games that I also replay frequently since the 80's are Donkey Kong (Coleco Vision, Wii, 3DS, Wii U), Donkey Kong Jr (Coleco Vision, Wii, 3DS, WiiU), Pac-Man (Intellivision, Wii, 3DS, Wii U).
There are others, but not with as consistent replay over the years Final Fantasy (NES), Dragon Warrior (NES), Genghis Khan II: Clan of the Gray Wolf (Genesis), Gemfire (SNES), Legend of Zelda: A Link to the Past (SNES), Super Mario 64 (N64 & Nintendo DS), Dragon Force (Saturn), Iron Storm (Saturn), Call of Duty 2 (Xbox 360 & Xbox One).
Oh, and Madden 13 on Wii U which I've been playing since 2012, but only because EA never bothered to release another Madden on Wii U. I haven't bought a Madden title on any other system since, because nothing else compares to being able to draw hot routes on the gamepad (online play isn't important to me, I prefer human interaction with friends in my house over internet opponents who quit in the middle of games and play more like a game of NFL Blitz rather than a realistic football simulation. I don't care if I'm in the minority on that opinion). Instead, my friend and I have been playing Madden 13 most Friday nights since 2012.