First of all, you need root. I use CyanogenMod on my Nexus One.

To delete the application you hook up the shell:

adb shell
#cd /data/app
#rm com.amazon.mp3.apk

This removes the application but does not remove the system reference.

When you go to Settings > Applications > Manage applications you still will see com.amazon.mp3

To remove that system reference do this:

abd shell
#pm uninstall com.amazon.mp3

Hope it helps.

-Kristof