The "Famicom adapter" was in a handful of the earliest NES games. I believe the story was that Nintendo was falling a little behind in production of cartridges for the US NES as it launched in time for the holiday rush, and building the adapter and using surplus Famicom boards proved to be a financially feasible move.
You can find a list of the games that Famicom adapter in the
National Game Depot game list. I've also seen these adapters used in some of
Ben Heckendorn's portable mods. In particular on his article on the making of the
NESp, you can go to the second page and see a gyromite cartridge broken with the adapter showing.
Most of these famicom adapter games had a variant with a regular board inside, so no particular game is a sure shot.