Because this is a wiki topic, you can easily edit this list, as long as your forum account has at least a Basic status. Please keep it alphabetically ordered and take a look at the existing entries to see the data structure. If possible, please add fingerprints like this:
F-Droid Archive (official)
F-Droid’s archive repository, serving old versions of apps built and signed by F-Droid.
Number of apps: ~2270
Guardian Project Archive
The Guardian Project contains privacy-related apps.
I2P F-Droid Archive
I2P’s archive repository, serving old versions of the I2P apps.
IzzyOnDroid F-Droid Archive
Archive for the previous F-Droid compatible repo.
Note by Izzy: Currently it’s always empty, so no need to use it.
LibRetro F-Droid Archive
This repository has the old builds of RetroArch.
Number of apps: 2 (RetroArch, RetroArch AArch64)
microG F-Droid archive
Official F-Droid archive for the open-source implementation of Google Play Services.
Repo info: https://microg.org/fdroid.html
The lightweight YouTube experience for Android
Number of apps: 1
Unofficial Anime/Manga FDroid Repository (added/tested on 2020-06-25)
Archive of Manga Readers (other than Tachiyomi), Anime scrapers/viewers, Nekos (catgirl images) client, etc.
Repo info: https://animanga.efreakbnc.net/