I can’t really remember games that warmed me up to a genre that I didn’t like, but I do remember some that got me into the genre.
Point and Click Adventure: King’s Quest. I loved solving the puzzles and some of them were pretty obscure. I had a friend who also played it and we helped each other out.
Sports Sims: Microleage Baseball. I loved managing the Yankees since I was a big baseball fan then.
Racing Games: Test Drive. I remember the frame rate being pretty bad which made driving difficult, but I still loved it.
Turn Based Strategy Games: Empire. My friend and I would play until the sun came up.