The first time I heard Utada wasn't in fact, from Kingdom Hearts.
Back when EXODUS was released in 2004, You Make Me Want to Be a Man made its rounds on the UK radios, and became quite popular (this was before YMMWtBaM was released as a single in 2005 - maybe its popularity contributed to it being released as a single here?).
I instantly liked the song, and I remember downloading it and listening to it constantly. I then heard Simple and Clean when my friend did play Kingdom Hearts, and said "that's the same person!"
I then went and researched her a bit more, and gradually built up my collection of Utada MP3s. Now that I work I'm going to buy her singles on eBay etc. in order to get most/all of her stuff.
Obviously there are a few that can't be bought here (the Dirty Desire single/remixes for example, which I had to download because it's only available in the US), but I'm doing my best to have legit copies of her work.
But yes, that's my story haha.