A few ideas... Sorry if they're a bit older than what you're looking for, but I stopped listening to the radio around spring 2004 and only picked it up again this winter. But these songs made quite an impression and I think they would be remembered by pop fans.
'Sk8er Boi', Avril Lavigne (late 2002)
'Crazy In Love', Beyoncé (summer 2003)
'This Love', Maroon 5 (early 2003)
'My Immortal', Evanescence (late 2003 - it's a mellow song, but I don't think the participants in a belching contest would care, would they?)
'Superstar', Jamelia (late 2003)
See ya,
AnnaBtG.