Termux (Linux terminal) is super cool, and you can install a lot of cools programs through it as well. Add in the plugins for tasker integration/etc and it can be used for some pretty cool things (ie, use wol to wake up your computer when you get close to your house, etc).
There's so many I could list, I'll just mention 2 underrated ones I don't see mentioned as much:
LibreTube - Best YouTube client imo, has a very nice and modern interface, proxies videos through Piped for maximum privacy (No direct connections to Google are made), No ads/tracking, SponsorBlock + Return YouTube Dislikes, support for downloading videos, etc. It's everything I'd want and more out of a YouTube client.
URLCheck - Excellent app that allows you to preview what a URL is before you click it, includes tons of features such as scanning for malware, removing any tracking parameters, upgrading links from HTTP to HTTPS, etc. I can't recommend this app enough for the security, privacy, and general peace of mind it gives you.
Syncthing, which syncs my files between my phone and computer. I can rip a music CD on my computer and it's instantly sent to my phone so I can listen to it on the bus or wherever.
StreetComplete to easily contribute map data to the OpenStreetMap project, which also powers OsmAnd+ without knowing anything about OSM
KeePassDX for convenient and secure password storage including autofill (combined with Syncthing for syncing your databases this is a fully fledged password manager across platforms)
AdAway as a reliable adblocker for all applications which doesn't require root, but can use the benefits of rooting your device to increase its usefulness even more
+1 for all the NewPipe mentions, as it's extremely useful especially for background playback
Also OsmAnd+ is incredibly useful if you don't want to give your location data to Google constantly. The maps are equally as good as those of the tech giants and it gets expanded regularly with actually useful features, like most recently, weather data.
Its biggest strength however is the customisability in my opinion, because you can style everything according to your needs, starting at the overlay and the style of the map and going on at the specific level of detail and custom navigation modes.
Additionally, you can download maps of the entire world for free and they get updated regularly.
Only downside: There is no traffic data as of now, probably because it would be difficult to implement without processing user data.
It's also on the Play Store, but there the "+" version costs money and because the project in itself is commited to being open source I think it's important to list
Lastly, Termux really is the best terminal emulator for Android out there. It is extremely powerful, even allows sh hooks into system utilities like brightness and biometric login, and has great styling and widget support.
You can even install full Linux-OS's in a sandbox via proot!
I use KeePass and Syncthing, but for mild fun I like Lexica and StreetComplete.
Lexica is a word finding game on a grid with a timer, and it's very customizable (size of grid, min length of words, length of timer, etc). Words can and often do cross over themselves and run in all directions. Invariably I will miss stupid obvious words, and I'm always interested to see the list of missed words at the end. They provide definitions for the ones you just don't believe and have to click.
StreetComplete is a way to update Open Streetmap with goals and badges and all that gamification jazz. For an additional personal challenge, try updating house data without making homeowners look at you funny and/or call the cops.
Oh yeah, I use IITC-CE too, because Ingress is life. And Niantic can take a flying leap.
AppManager.
Super stable, feature-packed app that can do nearly everything with your apps.
AdAway.
No ads in apps. At all.
Simple utilities.
Just very good replacement for Google proprietary suite of apps. Good design, feature-rich, simple to use. Developer is really awesome!
I'm a LibreTube person myself, but only because I can't figure out how to access a YT channel's playlists in NewPipe. A couple of my subscriptions have unlisted videos that are in playlists (for example MLIG live streams). LibreTube isn't perfect though. I cannot fully disable the "Home" page.
I used to make a lot of use of Newpipe, and probably should get back to using it more, but I've admittedly been preferring to use the mobile site with adblock for a while now, only switching to NewPipe for video downloads, due to how often NewPipe was having issues (presumably caused by frequent Youtube updates). Is that better these days? I sure hope so, it's a lovely app otherwise that I'd love to use more.
As for my own favorite, it's hard for me to pick, because there's several I make use of daily. In no particular order:
Simple Keyboard - Has been my main mobile keyboard for years now.
Editor - Just a simple text editor, comes up surprisingly useful.
Diary - I personally use this as a dream journal, and it works well.
Simple Calculator - Does exactly what it says on the tin. For some reason, my new phone I got last year doesn't even come with a calculator, lol.
Simple Calendar; Simple Gallery - I prefer these to the default Android apps.
Simple Voice Recorder - I make music sometimes, so this is useful to hum a quick tune before it leaves my head.
TimeR Machine - I use this during daily exercise as a HIIT Timer.
I'd also recommend RedReader, but I can't in good faith do that anymore because of what's going on with Reddit these days. Haven't used it or the site much since June.
I'd say my favorite is probably Simple Keyboard just due to how often I use it (read: literally all the time, because it's a keyboard), but I've gotta give mad props to TimeR Machine. It's genuinely a really polished app, and even gives you a quick walkthrough on how to use it on first startup that's pretty helpful. It'd be neat to see more apps with those options.-
I haven't explored the other options too much yet but 90% of the time, my pad is running Librera FD https://f-droid.org/packages/com.foobnix.pro.pdf.reader/ which I think you have to pay money for at the Google store. It's a great document reader and I really like the musician mode.
I haven't been on fdroid in years but I and mostly my kid used use play this silly matching game called Doda the Explodad or something, themed after Doria the explorer
Neostore (I prefer that to f Droid)
LibreTube/NewPipe Sponsorblock
Aves Libre for gallery
Aegis authenticator for 2fa
Bitwarden
Fairmail
Doodle - live wallpapers
Liftoff for lemmy
Antimine - minesweeper
Mull/Bromite/Fennec/Chromium for browsers