- 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]