Android

Rooting

Magisk - A suite of open source software for customizing Android.

KernelSU - A Kernel based root solution for Android.

KernelSU-Next - An advanced Kernel based root solution for Android.

Application stores

Mobilism - Trusted Forum for downloading Modded APKs.
Requires Sign-up.

4PDA - Russian Forum for downloading Clean & Modded APKs, as well as discussion alike.
Requires Sign-up; Captcha Guide: #1/#2

SBenny - Another Forum for downloading Modded & Paid APKs. Has a point-based system which you can easily farm.
Requires Sign-up.

APKMirror - Website to download APKs dumped from the Play Store.

Aurora Store - Open-source Google Play Store client focused on providing privacy with a modern design.

F-Droid - Decentralized store for downloading libre (FOSS) applications. Material You client for the same.

Obtainium - App which allows you to install and update different applications directly from their release pages. Supports a lot of sources such as Github, Gitlab, F-Droid, Codeberg etc.

Browsers

Firefox Nightly | Fennec - Nightly and Stable versions of Firefox. Here's a Guide to add more extensions to Firefox Nightly.

IceRaven - Fork of Firefox which provides additional features, removes Mozilla Telemetry and adds more extensions to the current list, allowing you to make your own too.

IronFox - Privacy oriented and deblobbed Firefox fork which enables many features upstreamed by the Tor uplift project using preferences from the arkenfox-user.js project. Here are Automated patched builds with OLED dark mode support.

Cromite - Security oriented and hardened web browser based on Chromium that has an in-built ad-blocker.

FFUpdater - App for installing & updating various Firefox-based and Chromium-based browsers, with added automation capabilities.

Privacy & Security

ByeDPI | PowerTunnel - Powerful tools to bypass DPI (Deep Packet Inspection) and censorship. Useful to unblock websites without relying on VPNs.

AdAway - Open-source mobile ad-blocker with a focus on privacy.  
This app benefits from having root access.

Bitwarden - Open-source & self-hostable password manager. Material You client for the same, with better performance and additional features.

KeePassDX - Open-source password manager forked from KeePassDroid; allows one to store passwords in an encrypted database locally.

Optimization

Canta - Allows you to uninstall (almost) any app from your device, without root access.

Universal Android Debloater - Android Debloater, uses wired ADB to uninstall hidden OEM apps and bloat.

File Managers

MiXplorer - Fully-featured Android file manager that supports multiple cloud storages and server protocols.

Material Files - Android file manager with the Material You design, can also be used as an FTP server or an SMB/SFTP client.

SD Maid 2/SE - Powerful file management tool for Android that specialises in freeing up space and removing unwanted data.
SD Maid 2/SE isn't feature complete as it is an in-progress reimagination of SD Maid to work better with newer phones.

Round Sync - Fork of RCX; an Android port of Rclone that has the ability to manage files on several different cloud service providers.

Video/Music

Seal - Audio/Video Downloader GUI for use with yt-dlp's supported platforms.

Auxio - Open-source music player with a fast, reliable UI/UX without the useless features present in other players.

mpv for Android - Open-source media player that supports a wide variety of media file formats, audio and video codecs, and subtitle types.

VLC for Android - Another open-source media player which has the ability to play various media formats, network streams etc. along with other useful features. Mod which allows Monet theming for the same.

CloudStream - Open-source app for streaming and downloading media along with a fully-fledged extension system.

xManager - Manage and install all versions of the Spotify app, unlocking features such as ad-blocking and skipping tracks.

Seeker - Open-source Soulseek client for Android which supports various features such as downloading, searching, sharing, messages, chat rooms, port forwarding etc.

Murglar - Android client for playing and downloading music from services such as Deezer, SoundCloud, VK and Yandex Music.

Torrenting

LibreTorrent - Open-source Torrent client for Android.
LunaSea - Usenet/Torrent manager. Useful for those who utilize seedboxes.

Mods

Morphe / ReVanced - Android App patchers that provide patches to popular apps such as YouTube, YouTube Music, Twitter, Reddit and more.

Aliucord - Plugin-based Discord client mod for Android.
It only supports the last version before the React Native update (126.21)

AyuGram | Nekogram - Telegram Client with Ghost mode, Message history, disabled ads and more.

Miscellaneous

Lucky Patcher - Android app modifier which can be used to remove license verification, advertisements, change permissions, unlock in-app purchases etc.
This app isn't open source so giving it root access to use some of it's features is your responsibility!

GameGuardian - A game/cheating app for Android. Similar to Cheat Engine on PC.
This app isn't open source so giving it root access to use some of it's features is your responsibility!