Drip - Keeping track of menstrual cycles (If you have it lol)
Tempo - Music client for navidrome
Clima - Weather app
Telegram FOSS - Alternative to the proprietary client
Aegis Authenticator - 2FA app
A lot of the mainstream apps definitely have privacy issues. They often sell data about their users menstrual cycles which can theoretically be bought by anti-abortion activists/authorities on the free market to track whether someone might be pregnant.
An app that recognizes birds singing near you, all on device, and has an option to show a photo of the bird too. It's exclusive to F-Droid (not on Google Play), and the only bird recognizing app I know of that does it all immediately on your device (without sending it to a server). https://f-droid.org/en/packages/org.woheller69.whobird/
Organic Maps
Highly detailed OpenStreetMap maps local on your device. Wonderful for walking directions, as it has on-device routing and maps out walking pathways (which is something that even Google Maps does not do well) https://f-droid.org/en/packages/app.organicmaps/
This is the best FOSS keyboard that's under active maintenance. It even supports swiping, but that requires a non-free binary library from Google. (Maintained fork of OpenBoard.) https://f-droid.org/en/packages/helium314.keyboard/
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 😉)