Here are some useful applications. Feel free to add your own suggestions:
Aegis Authenticator is a free, secure and open source app for Android to manage your 2-step verification tokens for your online services.
AntennaPod is a podcast player that is completely open. The app is open-source and you can subscribe to any RSS feed. AntennaPod is built by volunteers without commercial interest, so it respects your privacy while giving you full control.
A simple calendar with events, tasks, customizable colors, widgets and no ads.
A Loyalty Card & Ticket Manager for Android
Easy and quick contact management with no ads, handles groups and favorites too.
Sync your contacts, calendars and tasks. Get live-access to your WebDAV Cloud files. All-in-one CalDAV/CardDAV/WebDAV solution for Android
Fully featured, privacy oriented email app for Android
An open-source keyboard for Android which respects your privacy. Currently in early-beta.
A premium app for managing and editing your photos, videos, GIFs without ads
Loop Habit Tracker, a mobile app for creating and maintaining long-term positive habits
Enabling communication between all your devices. Made for people like you.
OpenKeychain helps you communicate more privately and securely.
Organic Maps is a free Android & iOS offline maps app for travelers, tourists, hikers, and cyclists based on top of crowd-sourced OpenStreetMap data.
RHVoice is a free and open-source multilingual speech synthesizer.
A open source run tracker
A material designed music player for Android
Minimalistic audiobook player
A Material Design Weather Application
And of course, Open source lightning wallets with on-chain support