Take a look at Newsblur: There's a free tier, or you can pay for hosting, but at the end of the day the sources[0] for the software you're using are freely available so if the service fails, or the author makes changes you don't like, or you find yourself needing customisations that aren't appropriate for the author to provide, you can keep using the software by hosting it yourself or finding someone else to host it for you.

[0]: https://github.com/samuelclay/NewsBlur

You might also find the Franklin Street Statement[1] to be an interesting read -- it tries to set out a useful collection of ideas for services that respect the users' freedoms.

[1]: http://autonomo.us/2008/07/14/franklin-street-statement/