I would like to know if there is a way to use the API or a code sample to obtain the list of the users that unsubscribed (opt-out list).
You can obtain your Opt-Out list by performing a bulk export activity. Documentation can on how to do this can be found at the following link:
When supplying List ID, you will want to use the URI of your do-not-mail list:
Alternatively, if you prefer to parse the data yourself, you can retrieve a listing of email addresses in your Opt-Out list by performing an HTTP GET on the following URI:
Support Engineer, Constant Contact
I also wanted to mention that you can use Searching for Contacts by Last Updated Date (Synchronizing Contacts) which allows you search for all contacts that have been added to a particular list (including the optout/unsubscribe list) since a specified date . For example if you wanted to query all contacts that have opted out since June 1, 2010 you could perform an http get on: