The song that made me a fan was Sanctuary. I can't remember where I first heard it. (Not Kindgom Hearts II. I discovered it was on that game later)

Sanctuary was not my first song by her, however.
I had heard of her ages before that song was released; my first song was Sakura Drops.
I thought her voice was beautiful but I only found the song to be 'Okay.' I tried out First Love, but because I knew she was fifteen at the time, I couldn't take it seriously, and then I tried Simple and Clean which I hated. I tried out Traveling which I also hated.
So then I decided that while I liked her voice, I didn't like her music.

I hung out on a ton of J-pop forums during that time, and Utada was overwhelmingly popular. So overwhelming, that I eventually grew to hate her because I just got so sick of hearing about her SO much.
So for about five-ish years, I hated her. To the point where I even slammed her voice which I liked when I first heard it.

Then one day I heard Sanctuary and my immediate thought was: "Is this Utada? ... It CAN'T be Utada; this is WAY too great of a song to be Utada." and then, "It IS Utada. ... Does she have more songs like this?"

And from there I discovered Blue, Keep Trying, Making Love, and This is Love.
For a while I only listened to these five; but then I eventually grew to really like Deep River, including the songs mentioned above. I actually listen to Simple+Clean/Hikari and Traveling quite often. XD;