Independent app stores (with their own repository of apps)

• F-Droid. The gold standard of FOSS app stores.
• UpToDown, mostly Google Play's apps it seems, but also accepts submissions from developers. Run by Spanish company, not FOSS, but can be used without user registration.

Alternative front-end clients to F-Droid

• G-Droid

Simply front-ends to the Google Play store

• Aurora, FOSS client. Available from F-Droid
• Yalp, FOSS client. Available from F-Droid