Here are several:
On the racism of the original: Fear by Disturbed
Cera: Headstrong by Trapt, Welcome To My Life by Simple Plan, or Pushing Me Away by Linkin Park(on her relationship to her father)
Littlefoot: Saving Me by Nickelback
Spike: Nobody's Listening by Linkin Park
Ducky: Sweet Sacrifice by Evanescence
Petrie: Hero by Nickelback
Chomper: Crawling by Linkin Park
Ruby: Everything by Alanis Morrissette
Tria and Tricia, or Mama Swimmer and Ducky: In My Daughter's Eyes by Martina McBride
This list could go on and on

Songs to tribute the beautiful friendship of the beloved gang:
Photograph by Nickelback
I Turn To You by Christina Aguilera
Remember Me This Way by Linda Thompson Foster(makes me cry everytime)
You've Got A Friend In Me by Paul Newman(Littlefoot and Cera, preferably)