Pokemon Blue, Silver and Sapphire molded my taste for the JRPG formula and got me into anime.
Then there's Ocarina of Time and Wind Waker which were really influential in my childhood as great adventure games.
There's also the Harvest Moon games before they were relicensed as Story of Seasons and the Rune Factory series, which all kind of made me love the life sim aspect of games. Oh, and marrying interesting characters in the game too.
Oh, and who could forget Paper Mario? The first three, at least. Thousand-Year Door is still one of the best games in history period and nobody can convince me otherwise.
Honorable mention to Super Mario Sunshine and Galaxy. I know a lot of people hate the former, and I don't necessarily disagree, but I used to rent it in a local game rental shop for the weekend and I would play the shit out of it. Oh, and Budokai Tenkaichi 3 was the shit back in the day, way before Sparking ZERO.
Yeah, I had a lot of games I liked when I was a kid.