AccountKiller
The deletion option from the menu is unfortunately quite unclear. It's called 'close' (including deletion of your data), 'deactivate' and 'suspend'. However this is merely deactivation. For that, try this link: http://www.sonico.com/cancel.php
For termination, send your request to delete your account to: legal@sonico.com (source: privacy policy).
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 you can always contact Sonico 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 Sonico using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Sonico. Click the icon below to find out how.