AccountKiller
From their international FAQ:
"To terminate your account, simply send an e-mail to Customer Support (http://zazzle.custhelp.com/app/ask/~/how-can-i-delete-my-zazzle-account%3F) that contains your username and the email address associated with your account. Once you've done so, a member of our Support Team will disable your account and remove any products both public and private. The account will be deleted fully when our system processes the next batch of account removals."
For international Zazzle customers there is no mention at all about this termination service. A shame.
Direct removal link: http://zazzle.custhelp.com/app/ask/~/how-can-i-delete-my-zazzle-account%3F
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks: this can be found mostly in the Terms of Service/Privacy Policy; otherwise you can always contact Zazzle and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for Zazzle using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Zazzle. Click the icon below to find out how.