I'm not talking about minigames (which are common), and I'm not talking about game compilations, or games in which you can unlock another game and select it from a menu. I'm talking about games that, in the course of playing the game, you can play another game. I can think of a few examples. Probably the most famous one is Shenmue (and its sequel), where you can go into the arcade and play Hang-On or Space Harrier. In Day of the Tentacle, you can find a computer with Maniac Mansion on it, and play it. In Pitfall: The Mayan Adventure, you can play the original Pitfall. In Pac-Man 2, you can go to an arcade and play Pac-Man and Ms. Pac-Man (SNES) or Pac-Jr. (Genesis).
Anything else like these? It doesn't necessarily have to have been a pre-existing game, but I guess it has to be optional (otherwise it's not really a separate game, it's just part of the game), and it shouldn't be a minigame, although I guess there are borderline cases and there's not a concrete definition of "minigame". But, yeah.