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.