Definitely not "Star Spangled Banner", that note isn't the "highest note ever sung" like some people claim it is, it is only a G6.
Mariah's highest note (that we have heard) is a G7# on a live performance of "Emotions".
There isn't one song that showcase all of her octaves, but she uses the most octaves when singing these songs:
"Emotions @ VMA's 1991" (She hit her highest note to date, G7#)
"Emotions" (She hits an F7/F7# and goes as low as C3, that's showcasing 4 octaves)
"You're so cold" (C3-C7, showcasing 4 octaves)
"There's got to be a way"
"You and I @ Live performance 2002" (She goes REALLY low here, hitting a F2, her lowest note that we've heard to date)
"My All" (for the low notes, she goes as low as C3 and slightly reaches a B2)
"Bliss" (for the high notes)
"Vision of love"
"All In your Mind"
"Bringing' on the Heartbreak"
"Love Takes Time"
"O Holy Night"
"Anytime You Need A Friend"
"Dreamlover"
So basically she has went as high as G7# and as low as F2, which means she possesses 5 octaves (Only judging from what we've heard, of course), 5 octaves
is pretty incredible.