F-Droid is an open source software repository that provides a platform for developers to host their applications and users to discover, install, and update them. It is a free and open source Android app store that allows users to browse and download apps that have been developed by a variety of independent developers. The apps available on F-Droid are usually open source, and the repository is maintained by the F-Droid organization. The repository is updated regularly with new apps and security updates for existing apps. All apps are verified before being listed on the F-Droid platform, helping to ensure that users only download safe and secure apps. F-Droid also provides users with a way to get involved in the open source community, with access to source code and the ability to submit bug reports, feature requests, and even contribute to the development of some apps.
Best application and has many more applications to offer.
Same repository as F-Droid, but adds more information (such as author and other apps from that author) Github / Gitlab rating (?) AND release / rolling stages. At the time of writing this (January 8, 2019) G-Droid is still BETA but very functional, I personally use it (along with F-Droid).
Warning: "cracked" software is potentially dangerous.
Google Play Store
Aptoide
Yalp Store
APK Pure
APKMirror
Fossdroid
AppBrain
Aurora Store
Amazon Appstore
1Mobile
G-Droid
GNOME Software
APKUpdater
TorrApk
AppsAPK
Software Manager
ACMarket
APKProz
PandaApp.com
Soc.io Mall
Aptoide is not a free and open source software repository.