The Sklik PHP SDK by Michal Kuchta allows API interaction to access search advertising features. Library and examples available, in addition to a tutorial at https://github.com/niximor/php-sklik/blob/master/sklik_tutorial.php
This past Valentine's Day, DuckDuckGo announced via Twitter that their search engine had "received over 1,000,000 direct searches yesterday for the first time ever!" A major accomplishment for a search engine that is essentially unknown. And this search engine has an API.