Katamari Damacy - Asuka Sakai, Charlie Kosei -
Que Sera Sera: Just the absurdity of the lyrics is enough to make this one instantly memorable, but soon it's in your head and it consumes you.
Earthbound - Keiichi Suzuki -
Eight Melodies (Piano Version): This song is meant to be the theme of the various points around Earthbound, but the moment it really hits you is during a scene of childhood nostalgia, when Ness walks up a black and white hill toward the home of his memories. He walks inside and sees the crib where he was contained as a baby, and for a moment... you see everything he has loved and everything he has lost from taking this journey rolled into one instant. It's perfect.
Super Mario 64 - Koji Kondo -
Dire, Dire Docks: The allure of this track is summarized in three words... Dream Like Quality. It's an extremely relaxing theme that perfect captures the idea of a level filled with water, while capturing the awe and dream quality of the entire Super Mario 64 experience. It's just fantastic.
Xenogears (Creid) - Yasunori Mitsuda -
Creid: Summarizes everything I love about the console RPG in music. Wish the stories in RPGs these days could capture my imagination as much as this track does, but I digress
The Legend of Zelda (Various) - Hyrule Symphony -
Hyrule Field: If ever there was a theme in gaming that captured the whimsical childlike feeling of exploration that is so perfectly displayed by the gameplay in a Zelda game, it happens to be the theme contained within Zelda - Hyrule Field. Nuff' said. Get it today
Final Fantasy VII -
J-E-N-O-V-A Absolute and Aeris' Theme: I didn't want to have two different sections for this, but herein lies my favorite boss theme and my favorite [female] character theme. I love them both for great justice!
And there are others, especially within Final Fantasy 6, Chrono Trigger, Chrono Cross and... shit, there are a lot others. But there you go.