This is going to date me, but my most memorable gaming experience was playing Ultima VII: The Black Gate for the first time. I was in high school, and it was my first PC RPG I had ever played. The art (for its time) was incredible, and it was one of the first non-linear, open-ended worlds in the computer gaming scene. Almost like an early Minecraft, you could interact with your environment in creative ways - read books, play instruments, make cloth, use a sextant, bake bread! I was hooked after that. The storyline was great, not just a veneer to put over a combat system. You really cared about the characters. Other than your own questions ("Name. Job. Bye!"), the narrative was quality too.