While you may have to give up some creature comforts doing so, it’s relatively easy and straightforward to run an (almost – damn binary driver blobs and firmware) open source Android phone, with nothing but open source applications, through F-Droid, one of my major complaints with F-Droid is that it’s about as user friendly as trying to cut down a tree with a used toothbrush. There’s no popularity lists, every category is clogged up with nonsensical packages (to the average user, that is), and the presentation leaves much to be desired.
Fossdroid changes that, and presents all these open source applications in a much clearer and nicer fashion. It also adds popularity and what’s new lists, making it just a little easier to find the open source application you’re looking for. There’s still some things to be addressed, it’s a well-done website.