While I didn't use them and have no comments on their search quality I did admire Cliqz for their ambition. They were building and running their own index until earlier this year. (https://cliqz.com/announcement.html)

They open sources some components e.g. https://github.com/cliqz-oss/keyvi.

I think any long-term search engine competitor will eventually need their own index though DDG is doing well financially so far.