i tend towards horror games but here's a quick list of my faves by genre:

• survival horror: pathologic, silent hill 2
• indie horror: yume nikki/2kki, off, space funeral
• mystery: danganronpa, your turn to die, chzo mythos
• puzzle platformer: oddworld: abe's exoddus and soulstorm
• life simulator: animal crossing, harvest moon: a wonderful life

and some others by series:

• pokemon: emerald
• zelda: minish cap, windwaker, botw

i think of this list yume nikki, abe's exoddus and animal crossing were most formative! i don't get the opportunity to play video games too often anymore but if you are on desktop you have the opportunity to play the art game every day the same dream in your browser. you can also download it for windows and mac.