The only reason I put a late of 2002 in there is because sometimes radio stations even though a song single was released in 2002, it might just start getting heavy airplay in 2003.
Mine are (don't laugh) no order
"head strong" trapt
"bring me to life" evanecence
"i'm with you" avril lavgne

Eminem - The Sauce (from a mixtape)
Audioslave - Cochise
Missy Elliott - Gossip Folks
Justin Timberlake - Cry Me A River
Foo Fighers - All My Life
Nas - Made You Look
The Used - The Taste Of Ink
Jay-Z and Beyonce - '03 Bonnie And Clyde
Eminem - Lose Yourself
And yes, Avril Lavigne - I'm With You

"Times Like These" -- Foo Fighters
"Like A Stone" -- Audioslave

Rob Dougan - "I'm not driving anymore"

Broken Social Scene - Stars and Sons
Justin Timberlake - Cry Me A River
Justin Timberlake - Rock Your Body
Missy Elliott - Gossip Folks
The Tangiers - Keep The Living Bodies Warm
Eminem - Sing For The Moment
Avril Lavigne - I'm With You
Talib Kweli - Get By
Sam Roberts - Don't Walk Away Eileen
White Stripes - Seven Nation Army
Freeway - Flipside
Buck 65 - Phil
50 Cent - In Da Club

Was that actually released as a single?

My two faves right now:

Lifestyles of the Rich and Famous by Good Charlotte
and
Girl All The Bad Guys Want by Bowling for Soup

Only one real favorite. And an immediatel classic IMO. The truly sublime "Clocks" by Coldplay. Amazing song.

Brother Ali - Room with a View
R Kelly Ignition Remix
Slug and Murs - The Two
Aesop Rock - Daylight
Sage Francis - Makeshift Patriot

Yeah, there's a video for it.