During a late panel at San Diego Comic-Con 2013, where Trey Parker and Matt Stone also revealed their collective banhammer on DLC for South Park: The Stick of Truth, they were asked about their inspiration behind the game.
Their first response was "Crash Bandicoot 2" which caused an unapologetic laugh from the crowd (which makes me think our audience for GameRevolution Radio is much larger than I initially thought). But then Parker got a bit more serious about the question, stating that apart from Link from The Legend of Zelda and Paper Mario, another Nintendo classic was the main inspiration:
We're big gamers and I think what was inspiring the game was a lot more lofty than what we could pull off. I was a big fan of it and what I kept thinking in my mind was Earthbound.
I haven't played it again in forever, but I just remember something being about 'Oh wow, I'm a little kid in a house and there's my mom and I go outside my house and am fighting like an ant and a little mouse.' It started out feeling so real.
I kept having in my head 'Do I really want [it] to feel like that you are a little kid, and you're playing this game and bigger shit ends up happening?' But I really loved that feeling that EarthBound had of 'I'm a cute, little kid in my neighborhood and we're running around playing a game.'
Considering that South Park: The Stick of Truth might as well take place in Imagination Land, it almost makes too much sense that Earthbound is an inspiration. In fact, Earthbound may just be the inspiration for the entire TV series, minus the awesomeness that is Paula. (Why isn't there an Earthbound episode in South Park anyway?)