Musicolet (Free, Ad-Free, Offline)
Great offline music player, and while not Open Source it’s Ad-Free and fully featured. Comparable to Poweramp (Payed)
Termux (Open Source)
Terminal Emulator & Linux Environment. Can use it to setup a server on your Android device, or just install your favourite CLI Linux programs. Fast, Simple, Powerful
Virtual Virtual Boy (Free, Ad-Free)
Works really well, with support for various types of 3D (Including Red\Cyan). Comes with a handful of free Homebrew Games so you can play it right out of the box
KeePassDX is a password safe and manager allows editing encrypted data in a single file in the open KeePass format and fill in the forms in a secure way , requires no Internet connection and integrates Android design standards. The app is open source, with no advertising . KeePassDX - FOSS Password Safe | F-Droid - Free and Open Source Android App Repository
Orbot is a free proxy app that empowers other apps to use the internet more securely. Orbot uses Tor to encrypt your Internet traffic and then hides it by bouncing through a series of computers around the world. Tor is free software and an open network that helps you defend against a form of network surveillance that threatens personal freedom and privacy, confidential business activities and relationships, and state security known as traffic analysis. Orbot: Proxy with Tor - Guardian Project
OpenKeychain helps you communicate more privately and securely. It uses encryption to ensure that your messages can be read only by the people you send them to, others can send you messages that only you can read, and these messages can be digitally signed so the people getting them are sure who sent them.
I have found this works with Yubikey too, which has been really handy.