>> 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