>> F-Droid: Free and Open Source Software AppStore
Recommendations:
>> AdAway: Blocking ads
https://github.com/AdAway/AdAway
>> AfWall+: IPtables-based firewall
https://github.com/ukanth/afwall
>> XPrivacy: Privacy manager (req. Xposed framework)
https://github.com/M66B/XPrivacy
>> NetMonitor: Network monitoring
https://github.com/SecUSo/privacy-friendly-netmonitor
>> USB Mountr: Mount ISO images as USB thumbdrive to boot distros
https://github.com/Streetwalrus/android_usb_msd
>> Orgzly: Plain-text task/note management*
https://github.com/orgzly/orgzly-android
>> Syncthing: Folder cross-platform synchronization*
https://github.com/syncthing/syncthing
>> AnySoftKeyboard: Multilingual keyboard
https://github.com/AnySoftKeyboard/AnySoftKeyboard
>> OsmAnd: Map/Navigation
https://github.com/osmandapp/Osmand
>> Transportr: Public transportation
https://github.com/grote/Transportr
>> NewPipe: Youtube Client
https://github.com/TeamNewPipe/NewPipe
>> Shuttle: Music Player
https://github.com/timusus/Shuttle
>> FaceSlim: Facebook Client
https://github.com/indywidualny/FaceSlim
>> Twidere: Twitter Client
https://github.com/TwidereProject/Twidere-Android
>> Signal: Messenger
https://github.com/WhisperSystems/Signal-Android
*combined usage of Orgzly and Syncthing for cross-platform task/note management