Ooh, good one! I'll try to stick to the very basics that I've installed, different strokes for different use cases and all.

• MicroG — a non-Google framework to circumvent annoying GSF dependencies.
• DAVx5 — will sync calendars and contacts from your own cal/cardDAV instance.
• ICSx5 — helps add external ICS calendars into your calendar.
• Syncthing — keeps documents, pictures, etc synced between devices.
• KISS launcher — search based launcher. No bloat, no muss, no fuss. Everything else seems to try too hard after KISS.
• Fossify apps. There's a whole suite but I only use
  • Fossify calendar,
  • Fossify contacts,
  • Fossify SMS messenger.
• Fennec — a Firefox that passes F-droid privacy muster.
• K-9 mail — um, is this top grade email app named after the robot dog in Doctor Who? Affirmative.
• Open camera — so much better than a basic Android camera app.
• Authenticator Pro — 2-factor authetication (dunno why it's called "Pro", it's not like there's a paid tier)
• Obtainium — another app manager, for the fringe cases where an app isn't on F-droid but you trust its source enough to download it from there.

Edited to add:

• NewPipe! — third party YouTube player that puts a stick in Google's tracking and profiling.

Additional repositories

F-droid is great and all but its best feature really is that you can add other app repositories alongside the flagship one. IMO you absolutely need to add the following repos for the best selection (ie., adapted to my list above 😉)

• IzzyOnDroid
• MicroG
• NewPipe

Suggestions for more repos?