Formerly Amazon Underground, the Appstore is Amazon’s storefront for Android apps. Get it here. Many apps that are region restricted in the Google Play Store can be found in Amazon Underground.
Official Non-Play Store Releases
Here are some excellent apps that are available officially from their developers outside of the Google Play Store. You can even pay for their premium versions if you’re unable to buy apps in the Play Store.
Web Browsers
Mozilla Firefox (Direct, x86)
Dolphin Browser (Direct, Amazon)
Opera (Amazon)
Flash Player (Direct)
Messaging
WhatsApp (Direct, Amazon)
Viber (Direct, Amazon)
Media
VLC Media Player
Kodi (Formerly XBMC)
KoRe (Kodi Remote)
Other
Nova Launcher (Direct, Beta)
Utilities
Teamviewer (Direct, QuickSupport, Meetings)
Acrobat Reader
Vysor
RAR for Android
G-NetTrack Lite (Direct RAR File)
Root Tools
ClockworkMod Helium Backup (Direct, Desktop)
ClockworkMod ROM Manager (Direct)
JRummy Ad Blocker (Direct)
Titanium Backup (Direct)
APK Mirror Releases
APK Mirror is the only unofficial repository of Android apps copied from the Google Play Store that I trust. I have used numerous apps from this site myself and have never encountered security issues. If a popular app that you like isn’t available in your region from the Store then you can probably find it on APK Mirror. Here are some i find noteworthy.
Microsoft Office for Android
 Word |
 Excel |
 PowerPoint |
 Outlook |
 OneNote |
 OneDrive |
 Skype for Business |
 Keyboard for Excel |