Aight, I'mma word vomit about all the games that blew my little mind away, here we go! (spoiler free)
Mother 3
Probably the first game to make me cry and tell me such a beautiful story, and that challenged what a story could mean for me since I experienced it at like age 10-11. Obviously, that meant I watched Chuggaaconroy's LP of it, but Mother 3's story is seriously one of the most important stories to me, and probably helped me grow up in ways invisible to me. God bless this beautiful game.
Xenoblade Chronicles (Wii)
The first game to show me how truly astonishing a game can be, and I played it in a really formative time in my life when I was just starting to be come a real person (age 13-14). The sheer scale of the game was life-changing for me, the music and visuals astonished me even on the Wii version, and the point from Prison Island onward, to Mechonis, to the end of the game, was utterly revolutionary to me, showing me the majestic potential of storytelling in video games. I hadn't played JRPGs or VNs at that point yet so the plot felt so new and mind-opening.
Ghost Trick
A heartwarming, moody, mysterious paranormal detective game on the DS that oozes charm and style, but the further you go in, oh man, lets just say that the final act of the game where all the questions are answered and everything makes mindblowing sense, agh, such a satisfying well-told story!
9 Hours 9 Persons 9 Doors
Shortly after Ghost Trick, I experienced 999, and god, the off, tense vibes, the likably hateable characters, my first experiences with an Uchikoshi story with those Uchikoshi plot-twists, 999 is such a special story to me. I also adore the sequel Virtue's Last Reward and even Zero Time Dilemma a lot, but 999 is the one that captures my heart the most, the most satisfying story on its own.
AI: The Somnium Files
Probably the most recent game to capture my heart for its characters and good ol' Uchikoshi mystery and plot twists. Where Zero Escape lacked in the charm/character department, this game absolutely made up for it while maintaining the same storytelling prowess. Dear god I love this game and I can't wait to play its sequel hopefully soon!
Other Super Important Honorable Mentions
Danganronpa series (first experience with a death game genre when it was still new and not done to death. The mystery really captivated me despite the series' flaws)
Ace Attorney series, especially the Takumi ones (lovely characters, lovely stories, particularly love AAI:2 and DGS, can't wait to play DGS2 soon hopefully!)
Dayshift at Freddy's (my current beloved, for its characters primarily with themes of family that make my heart go warm and hurty)
13 Sentinels: Aegis Rim (SUCH a satisfying game to play through and try to puzzle out. While the overall plot is just "great" to me, the JOURNEY to getting there is SO captivating man, I just love me a good, addictive mystery leading to exciting plot twists, and this game is absolutely loaded with them!)