How to remove your Ubuntu One account
Use their webform to request removal, right here: https://one.ubuntu.com/help/contact
For more info (including paying members), read: https://one.ubuntu.com/help/faq/how-can-i-delete-my-account/
Helpful Trick: Removing online data
Publicly visible text/images often aren’t properly removed even when you succeed in removing an account. Try editing or removing them manually before removing 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 Ubuntu One and ask personally. By the way, removal requests don’t necessarily mean your data will actually be removed (e.g. due to legal obligations).
Helpful Trick: Remove third-party logins
If you signed up for Ubuntu One using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Ubuntu One. Click here to find out how.