Earthbound is, to put it lightly, weird. The main character is a little kid, the locations are varied (mole caverns, small town in the grips of an insane cult that worships the colour blue, land before time -ish area featuring gigantic dinosaurs), and the enemies are hilarious. You fight things like "Big Pile of Puke," a "Manly Fish," and "Cute Li'l UFO." Your weapons can include frying pans and baseball bats. The goal of the game is to stop an evil alien from taking over the world.
The first diary I ever kept included painfully detailed accounts of playing Earthbound - there's a page where I list what areas there are (this is directly before a one-page story written from the perspective of an anthropomorphic dolphin), and I wrote almost daily about where I was in the game and what was happening. Clearly something about this game really clicked with 11-year-old me, but I've also really enjoyed all the times I've re-played it. I recommend it to anyone who's interested in RPGs.
And the music is great - last year I, along with the Bath Haus Klezmer Band, tried covering this song. Enjoy!