One of the things I struggle is to discover new or popular apps, because of the lack of stats on f-droid (privacy first, I'm not complaining).
So I'm interested on the community knowledge.
For me the best ones are:
Syncthing (device synchronization over LAN or internet without a centralized server)
Saw another post similar to this and commented there, thought I would paste the reply here too - Please remove my comment if it's against the rules.
The foss apps I use and love on my android are these in no particular order -
Fennec Fdroid - I know there is Mull, but I just use this with a Custom Add On Id. Ublock Origin and Local CDN are great.
Simple Gallery Pro - I used the paid Play Store version, but you can get it from F-Droid. It's great.
Aves Gallery - I have been using this alongside Simple Gallery for it's looks mostly, and you can also select "favourites" that are marked by changes in metadata (if I am correct, otherwise please let me know), so even if you mistakenly uninstall the app or move the photos, the metadata makes the favourites reappear. You can also "rate" your photos here. A fantastic gallery app in itself, particularly if you want to organise your photo.
Librera Reader - In my experience the most feature rich and complete foss Epub Reader. Supports all other majore file formats too. Great app to read on with no fuss.
Rethink Dns - A VPN based adblocker and tracker blocker. Used to use Blokada before, moved to this one. Fantastic with a lot of customisable blocklist and an option to individually block or allow domains, both system wide or on a per app basis.
Fdroid - I just use the good old fashioned official App, but I have heard great things about Neo Store (I hope I am correct with the name). Gets the job done, and I just stick to it.
Open Camera + Libre Camera : Both fine open source apps for taking Photos and videos. Open Camera is more old and reliable, but I also enjoy Libre Camera. Both are fine for what they do.
VLC Media Player - For songs and videos both. There are better options for music but it gets the job done and I need a single app only.
Collabora Office - I sometimes need to type long stuff, but do not have access to a PC or Laptop. Just an otg and a keyboard with my phone gets the job done again.
Pineapple Lock Screen - If your phone does not have a "double tap to lock" this one is just fantastic to have.
Mulch - A Chromium based web browser for when you really need chrome-like interface. I just use it because it's nice. Fennec is usually enough. Do note that Mulch does not block ads, so it's best to either change the dns or use a system wide adblocker. Also better to use the DivestOs repo to get fast updates.
So, yes, these are the ones I love and regularly use. Special mention, I haven't used it in a while but AntenaPod is great for Podcasts, Infinity for Reddit (sad) for Reddit, K-9 Mail as an Email app, and Markor as a note taking app with Markdown support are all great. If you use YouTube Newpipe is all you need.
Thank you if you read through all of that. I have not written this much in a public forum for a while. Have a wonderful day :)