How do you get banned from Neopets?

Answer 1

If you create a ton of accounts to spam or otherwise abuse, you will be IP-banned so that you are not able to create more accounts, though this is not especially effective because IP addresses can change with relative ease.

Answer 2

Cheating or breaking any of their rules. If you do not want your account, just don't get on Neopets, or self-freeze the account.