I got ridiculously into Fire Emblem for GBA despite not caring about JRPGs at all and finding handheld games uncomfortable to play. Though the strategy-game elements and having a Game Boy Player probably helped with that.
I beat the game like five times--I imagine well over 100 hours playtime total--and even went through the mind-numbingly tedious process of getting support conversations. I got like 2/3s of the supports by the time I was done with the game. I even enjoyed the storyline despite my usual aversion to anime tropes. Despite getting into that game, though, I did not enjoy the other Fire Emblems nearly as much. They all felt like imitations of that game, and I had already burned myself out on the GBA one.
Also, despite not caring about sports, I played an assload of NHL 94 for the Genesis.
Sometimes, playing a game outside your comfort zone can surprise you.