To get things going here and also because I'm interested in what kind of fun stuff you're running on your phones, I'll post a list of apps that I'm using daily or that are part of my Android experience.
To start it all off, I'd like to emphasize that I try to run FOSS apps almost exclusively and I also don't use Google Play Services whatsoever (not even MicroG). I do run some very few closed source applications in a separate profile with Insular, but I plain out refuse to run them if they flat out require Google Play Services.
Feel free to tell me what YOU are running in the comments!
My installed Apps
AdAway | Blocks ads by utilizing root access or by acting as a local VPN**
Aegis | Provides 2-factor authentication codes, includes a repository of icons for your services
Aurora Services | Required for background installations with Aurora Store****
Infinity for Reddit | Feature-rich Reddit client (future uncertain due to Reddit's API-pocalypse, however, you can compile Infinity with your own API, as described here)
Insular | Creates a separate (work) profile where you can install "big brother" apps**
Noice | Create and play back profiles of overlapping noises to drown out environmental noises (use version 1.3.3, version 2.x requires internet access and an optional subscription)
SlimSocial for Facebook | Wrapper for Facebook's website, so you can interact with people that refuse to use any kind of messenger, but are still present on Facebook
SuperFreezZ | Freeze applications that you're not using***
Open Camera | Feature rich camera with Camera API v2 support, usually the best FOSS camera on 3rd party ROMs
*CAN be used as a client for self-hosted services
**Offers additional features if root access is present
***Requires root access to be present
****Part of a Magisk module
Edit: Added some links and changed Infinity's description
Great list - picked up a couple new ones for myself. Thanks.
Adding to your list:
Paperless Mobile An almost fully-fledged mobile app for my Paperless-ngx server
Syncthing Helped me (with Photoprism) replace Google Photos, but also syncs backup files made by other apps (Tasker, Signal, calls & texts, etc) from my phone to my computer overnight
Simple Search Completely configurable search widget, lets me search with my private Whoogle servers from my phone's home screen
Shelter A lot like Insular, lets you utilise work profile for your own needs - apps, files, etc.
Indeed I do. It's not necessarily something I find myself using every single day, but it's come in handy on so many occasions, I can't imagine NOT having it now. I'm (slowly) scanning all my existing paper archives in and shredding them, only keeping the physical copies of things that make sense (eg. birth certificates). The more data I put into it, the more useful it is.