A selection of F-Droid apps:
- AFWall+ (firewall, useful to block traffic to limit mobile data usage when I still need to enable it)
- Amaze (File Manager)
- AndIodine (Iodine client, use internet through wifi guarded by captive portals that still let DNS queries pass)
- Barcode Scanner (scan QR and bar codes, share things through QR codes)
- Clementine Remote (control the Clementine music player)
- Draw (to write scores when playing games)
- Easy xkcd, Simple Dilbert for comics
- E numbers, OpenFoodFacts (to know what you eat)
- Clip Stack, a Clipboard manager
- DAVx⁵ (formerly DAVDroid), to synchronize contacts and calendars with a Nextcloud instance (or any CardDav / CalDav provider)
- ForceDoze (to force the phone to really sleep when the screen is off)
- Drowser (to kill chosen running apps when the screen goes off)
- Document Viewer and PDF Viewer Plus to display PDFs. The former seems to segfault quite frequently but is nice when it works.
- Fennec or Icecat (Firefox Mobile)
- ForRunners (to keep track of running sessions, offline)
- LogCat Reader (to show Android's debugging log)
- LibreOffice Viewer (useful when people send office documents by mail) - K-9 Mail (Mail client)
- Maps and OsmAnd (for Offline GPS), OpenVegeMap (helps finding places where to eat)
- NextCloud (access files from a NextCloud instance, auto upload pictures)
- OpenCamera, a nice application for taking pictures. Works better than Lineage's stock app on my phone.
- oandbackup: backup data and applications.
- QKSMS: a really nice SMS app that is able to synchronize with the default Android SMS app, which is important for me for backups
- Riot.im (not using it at the moment though)
- Red Moon, which I use to make the screen even darker (and it works well with an AMOLED screen). I don't actually use it to filter blue light.
- SMS Backup +: to backup SMS and call logs to an IMAP account. I also copy files from /data/user_de/0/com.android.providers.telephony/ for that, which provide a perfect backup, MMSes included.
- SatStat (to debug GPS, and show a compass)
- Sky Map, to see the stars and constellations.
- Sound Recorder
- Termux: provides a GNU/Linux like environment, and a great terminal emulator which can be used with a real GNU/Linux distribution installed in a Chroot or from SSH.
- UnicodePad (look for unicode characters / emojis)
- VLC (a good music and video player)
- 2048, Open Flood, PipePanic (games), DroidFish (chess)
XServer XSDL is a good free X11 server for Android that is unfortunately not in F-Droid but now there is an X server in F-Droid (which seems to have less features).
Etar looks like a good calendar app. I've come across Wi-Fi Reminders, which can be used to display notes when connecting to a particular Wi-Fi, which seems nice and useful. There are apps to avoid leaks when using Wi-Fi. And also notes / tasks apps that I don't use regularly.
TrebleShot looks nice to exchange files between devices.
[edit : added oandbackup]