F-Droid - F-Droid is an interesting alternative for Android users who want to try something different and not have to use the Goole Play store all the time.
Mammudeck - Mammudeck is a TweetDeck-like columnar interface to Mastodon/Pleroma.
Aurora Store - Aurora is a FOSS Play Store client that does not require a Google Account to download directly from Play Store. However you can login with your Google Account to download your already paid apps!
Code4Freedom - The liberty based app store.
Aptoide - Aptoide is a third party replacement for the traditional Google Play Store.
Apple App Store - Install apps on your iDevice via the App Store.