I'm a fan of the following apps and use them almost daily (in no order):
addy.io - email aliases
Amaze & Fossify File Manager - cant decide between them
Aurora Store - Less privacy invasive version of the playstore app
AyuGram - "Just an exteraGram based client with TOSS breaking features in mind"
Bitwarden - Password manager
Brave - popular browser, backup
Calculator++ - scientific calculator but beware of the playstore version, it's full of ads & trackers (FD version is fine)
Fossify Calendar - mainly for the widget
Clock You - better clock app and nice widgets
Cromite - another browser, this one's just for Facebook
Currencies - currencies
Simple Draw - I have tried multiple drawing apps and I keep returning to this one despite the project being deprecated
Droid-ify - F-droid client. Neo-Store is nice too!
Eddie - AirVPN client
FairEmail - email client
FFShare - compresses images
Filen - cheap and E2EE cloud storage
Fossify Gallery - best one out there
GMaps WV - for when OsmAnd cant find that one location
HeliBoard - keyboard and the only one with autocorrect
Image Toolbox - edit images in many different ways
Leumroid - emulate old classic games
Lexica - fun words game
Librera - fully-featured Ebook reader. Get the F-droid version for the pro version
LibreTube - Youtube
Lona - snake game with a twist
Materialrious - Youtube but doesn't always work
Metro - music player
MJ PDF - simple PDF viewer
Molly - better Signal client
Mull - hardened Firefox browser
Muzei - wallpaper app, plenty of add-ons available to download
Next Player - great video player
Noice - background noise
Notally - simple notes app
Obtanium - automatic updater from Github
Open Camera - camera app
Open Link In Browser - if you've made it this far you've seen I use many different browsers on my phone and this app helps me choose one when I tap a link
OpenBoard - I only use it for its spellcheck because HeliBoard's seems slightly slow
OsmAnd~ - maps
RedReader - Reddit client, no idea how it still works but it's better than the official app even
RetroArch - emulate more games than Lemuroid but requires more setup
SAI - install .apks and .apkx
Save to - when you "share" a file but you just want to save it
Scrambled exif - choose this app from the share menu to remove all exif from a photo
Shattered Dungeon - rogue-like RPG
Shop with mom - find the best value for your money while shopping
Session - E2EE messaging
SimpleX - also E2EE messaging
Simple QR - QR reader
The Light - bible app
The Life - another one
TranslateYou - translator
Tuta mail and calednar - my main email client
UntrackMe - removes trackers from links
Voice Recorder - voice recorder
Wall you, Wallman, Wave Line- wallpaper apps
Breezy Weather - weather app
Wikipedia - Wikipedia
ZipXtract - extracts zip, rar, etc.
I do use many other non-FOSS apps