Here's a (growing) list of the most common reasons why auto-subscribing to MailChimp could fail.
Wrong MailChimp API key / List ID
First and foremost, kindly double check you have provided a valid MailChimp API Key and a valid List ID.
MailChimp account is not confirmed yet
In case the Double-Optin option is enabled, no user will be added to the MailChimp list until they have clicked on the confirmation email sent by MailChimp.
Required Merge Tags are missing
Make sure you've mapped in the Data Map option the required Merge Tags of your list.
Joomla account is not confirmed yet
In case the Force User Subscription option is disabled, no user will be added to the MailChimp list until the Joomla account is confirmed.
MailChimp could have a slight delay sending the confirmation email or even adding the user to its database. Please just be patient and make sure to check your SPAM folder.