The obvious ones that spring to mind are Mozilla, DuckDuckGo and ProtonMail, but does HN have any other examples?
Threema and Signal for messengers.
They seem different to other search engines in that they actually have their own index rather than just proxying to another engine (e.g. Bing)
https://www.mojeek.com/ https://blog.mojeek.com/2020/12/frequently-asked-questions-a...
Other search engines mentioned here, and many more, are primarily syndication partners of Bing (mostly), Google or Yandex.
https://www.searchenginemap.com/
https://element.io/