I use Syncthing to sync my phones photo library with a Google Pixel running on my server rack. If you didn't know, the first model of Google Pixel still gets unlimited full quality photo uploads to Google Photos for free, so its a great way to keep those backed up, even if I don't particularly enjoy the company they're hosted on.
Tailscale: easily allows for setting up a mesh VPN network, completely unbothered by firewals and NAT. Sometimes I fix stuff on my homeserver from my phone with Termux.
Tachiyomi: great manga reader, I only hope that sync gets officialy built in (I'm already using SyncYomi).
Revolution IRC: IRC client.
Nextcloud: backs up photos on my homeserver instead of Google Photos. Sadly uses a lot of battery, probably because I have around 50K images to scan.
Jellyfin: streams shows and films from my homeserver.
Revanced Manager, a YouTube(+more!!!) patcher to remove, er, unwanted features.
Bitwarden Password Manager, password manager I switched to when Lastpass went down the shitter and wanted me to pay. I even ended up paying 10/y for TOTP in bitwarden, but only because I felt they actually deserved it, unlike lastpass
Mull, A Firefox fork with privacy enhancements, free modifications, and extension support. Mozilla, Firefox, and the Gecko engine help to fight the Chromium monopoly, which powers browsers like Chrome, Edge, Opera, Vivaldi, etc.
Termux, terminal emulator for Android. I really only use it in conjunction with Tasker (nonfree), but still useful for one-off applications
K-9 Mail (soon Thunderbird for Android!), the only mail client for Android Ive ever used (apart from the gmail app). Now owned by Thunderbird and excited for it's future.
KeepassDX, newpipe, tusky, open board, Firefox, infinity(not for long sadly), jerboa, jellyfin, si gnal, f-droid, exodus, binary eye.
All that on my phone.
My computer runs fedora and I'm not changing anytime soon.
Patcher for YouTube which adds AdBlock/Sponsorblock/Other various features. Also supports other apps, such as YouTube Music. This is a must if you use YouTube on your phone.
Installer for modded Spotify. Includes AdBlock, unlimited skips, and the ability to play any track on demand, using a free Spotify account. (The installer itself includes an ad that plays when downloading the patched APK, but this can be disabled in the settings of xManager)
Storage utility/manager that's actually good, unlike 99.99% of cleaner apps on the play store. Pro version is free on GitHub, make sure to support the developer if you like the app.
Antennapod, KDE Connect, ... way too many to name.
F Droid (in my case Neo Store) is a great place to search.
If I search for a certain use case, I check out this Github Repo that lists very good FOSS apps
Almost everything what I use is already listed here (Termux, NewPipe, Joplin, etc), so, here's a few small apps that no one has mentioned yet:
ViMusic - a tiny accountless app to stream music from YouTube music.
HTTP Shortcuts - an app that allows you to create home screen shortcuts that execute arbitrary http requests, it supports JavaScript, so, you can write even something pretty complicated.
I won’t be using Android for a few years till my Apple device dies (best phone is the one you have, right?). However, there is one app that you can use cross platform that I endorse completely: KeePassium .
Has a simple interface, supports password sharing between self hosted servers via standardized KeePass libraries, and has TOTP which eliminates the need for a second app. I use keepassXC on Fedora and it syncs wonderfully. Took a second to setup, but it’s the best password experience I’ve had thus far.
My Expenses: pretty much the best expense tracking and budgeting android application I've had the pleasure of finding, It has some paid plans to enable cloud hosting, a local web server, among others, but the free one was more than enough to me for years.
My most useful is probably ntfy & my matrix client, Element. I self-host ntfy & a matrix dendrite server with some bridges. I am able to receive notifications from all of my chats without Google services installed, as well as notifications from Tusky thanks to Element and Tusky's support for UnifiedPush.
Transistor a very basic app to listen to radio over internet. Previously I was using RadioDroid which is more advanced but for what I do a simple app is largely enough and better
an open source notes app of course, an opensource keyboard app, there are a lot of good things in those categories. also, back when i read ebooks on my phone i found a really good app called comfort reader that automatically reads books for you and stuff, and there are also other great reading apps
Thumbkey: A keybord with a vastly different layout designed for ergonomy. I'm realy happy about this one because the only atlernative was closed source.
syncthings-fork to backup my files
SD contacts on fdroid to export my contacts on change in a folder for syncthings to backup. ( I changed the code of this one to use only one file instead of several ones)
kde-connect: allows sharing notifications,
files, and much more between your phone and pc
On my Android tablet, my most used app has got to be either Mull (web browser, based on Firefox), NewPipe (YouTube client), or Tusky (Mastodon client).