Android

• AdAway -- system-wide ad-blocker, works with and without root, but Adguard DNS work well enough so don't bother if you can't root.
• Aegis -- clean OTP app
• AntennaPod -- best podcast player with lots of customisation
• Breezy Weather (requires IzzyOnDroid repo; fork of the abandoned Geometric Weather) -- brilliant, beautiful, ad-free weather app with Accuweather data
• CloudStream (IzzyOnDroid) -- 🏴‍☠️ video streaming from all over the web
• Doodle Live Wallpaper -- FOSS recreation of Google's Pixel wallpapers with some extra customisation
• Frost for Facebook -- pretty web wrapper for browsing Facebook
• LibreTorrent -- FOSS, ad-free torrenting app
• OsmAnd+ -- OpenStreetMap client with navigation, offline maps and loads and loads of customisation
• Antimine -- infinite minesweeper game
• Neo Backup -- root-based app data backup
• SimpleAppDowngrader -- root-based, allows downgrading apps without uninstalling and retains data files
• Tasks.org -- best tasklist available, self-hosted but also works with Google Tasks
• ViMusic -- free YouTube Music client, works flawlessly and is very pretty
• Wave Lines Live Wallpaper -- customisable wave lines live wallpaper

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.

OsmAnd~

Makes navigating around easier especially as someone who likes walking.

Edit because somebody mentioned about the lack of description and link of apps:

OsmAnd~ is a FOSS alternative to Google Maps and uses OpenStreetMap for its data. You can download it here.

Unciv is a fully-fledged Civilization clone. It's honestly insane that such a polished game is not only free, but also open source.

https://f-droid.org/en/packages/com.unciv.app/

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.

• Newpipe (adfree YouTube client)
• Thunder (responsive Lemmy client)
• Geometric Weather (great weather app)
• FBreader (low resource eBook reader)
• KDE connect (sync between phone and laptop)
• Glider (HackerNews app)
• Orgzly (needlessly complex org-mode renderer)
• Skymap (Position-aware constellation viewer)
• Open Camera (impressive photo app)
• PianOli (fun piano app)
• Moonlight (game streaming client)
• WLANScanner (find hidden WiFi camera/devices/networks in hotels)

TLDR:

• NewPipe for YouTube playback

• OsmAnd+ for great offline maps with lots of customisability

• Termux for terminal emulation and ssh

• 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!

edit: add even more great apps