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
It's very interesting that OP doesn't use microG. How do you deal with no notifications? Do you use apps with custom (non-google) notification support? What are the disadvantages?
Here's a list of apps I use that are not on OP's list:
Compared to OP, I do use MicroG with LineageOS. I also use quite a few closed source apps (banking apps, uber-like, car/bike sharing, some local apps for public transport, chatting apps, navigation, etc) but I do try my best to avoid them if I can. From time to time I log into Facebook / Instagram or use Google Maps in the browser, but don't have the apps installed.
Hey, thanks for your list! Very interesting. I used to use ACCA, too. But due to me not using that many apps (especially only very few closed source apps) and therefore not having many background processes, my batteries are always very healthy. My phones usually last around 4 years and never once has a battery failed on me, despite me regularly charging and discharging my phones almost completely every 1 1/2-2 days. ACCA is a good piece of software, but I feel that I don't need it. Funny enough, my old phone (Xiaomi Mi MIX 2) still works the whole day when charging it during the night, but what made me ultimately get a new phone is that the screen had burn in issues and the volume and power buttons acted up from me using it so much.
I also used to use GadgetBride for my Mi Band, but after some weeks, I usually take my band off and then it collects dust for months. Don't know why that is, though.
I wish I could use OpenBoard or any other keyboard. I need Japanese input and I want to have it in one single application. Right now, only Microsoft SwiftKey is able to do that for me in a convenient way, which means, I have it installed and completely cut off from the internet, due to it being closed source. Another thing is that I use Insular for closed source apps in a work profile and a second installation of SwiftKey there has native support for syncing settings and dictionaries with the one on mainland.
I personally don't care for Signal at all. I know, Telegram isn't private, but I'm making a compromise here. I really like the UI / UX of Telegram. Something where Signal lacks. It's all a matter of taste, but I just don't like it. Also, all my friends and family are either on Telegram or on WhatsApp.
Regarding me using no Google Services Framework or MicroG at all: I don't need them. No truly FOSS app will utilize that. They all handle notifications on their own. The few closed source apps I use (including banking, etc.) are on my Insular space and they don't need GSF also. If I try to use a closed source app that straight out requires it or crashes when no GSF is present, I uninstall it immediately. Simple as that.
Lots of great recommendations and I got a few ideas from here.
I came here to mention AFWall+, which blocks apps' internet connection with iptables for that additional layer of security.
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.