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