This is a really tough one. I'm inclined to say the Tales series, specifically the Team Symphonia games (all the games barring Legendia that came out in America from Symphonia to Vesperia) , because that's how my brother and I met some of our current best friends back in Middle School. If I had to narrow it down to one, I'm gonna say Abyss if only for it being my second favorite Tales Game (Tales of Destiny R being the first).

A close runner up is Fire Emblem Blazing Sword for teaching me that games with menus can still be fun and engaging (I remember being disappointed FFX didn't play like Kingdom Hearts until I noticed that each character had a specific role akin to Fire Emblem. If not for that game, I probably wouldn't be on this forum today.