The F-Droid Repository is an easily-installable catalogue of free and open source apps for Android. With F-Droid, it's easy to browse and install apps on your device, and keep track of updates. You can also browse the repository with a web browser, and download the app...
Aurora Droid is an unofficial, FOSS client to FDroid and FDroid-compatible repositories with an elegant design. Not only does Aurora Store download, update, and search for apps like the Official FDroid client, it also empowers the user with new features.
This is an F-Droid style repository for Android apps, provided by IzzyOnDroid. Applications in this repository are official binaries built by the original application developers, taken from their resp. repositories (mostly Github).
The project's aim is to promote free and open source software on the Android platform. Fossdroid takes its data from F-Droid, but organizes apps in an attractive, Google Play-like arrangement with the ability to view apps by popularity.
APKLinker has download links of popular Android Apps. You can just sideload your favorite android app. Either it's final, beta or alpha, you can get all variants of android apps here.