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...
Google Play (formerly the Android Market) is an online store by Google for Android devices. Browse and search for apps, books, and movie rentals from your web browser or Android device.
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.
Aptoide is a distributed marketplace for mobile applications which runs on the Android operating system. In Aptoide, unlike the default Google Play Store, there is not a unique and centralized store but each user manages their own store.
APKPure is a totally free APK downloader for Android phone and tablet. Download apk directly from Android market even without Google play store account.
In an effort to make things easy, and maybe even fun, AndroidPolice.com created APK Mirror. Over the past several months, they've been working to build a smooth, reliable, trust-worthy site to host the downloads users love.
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).