I'm not sure if they're popular or not but I didn't see them mentioned in this thread and I rely on these fantastic open source apps daily:
- AntennaPod -- podcast app
- Orgzly -- Todo lists / reminders / notes via org files. Can be synced via syncthing.
- Aves -- gallery app
- KeePassDX -- keepass client
- Prognoza -- weather app
- Olauncher -- minimalist launcher
Honourable mention: Harmonic -- hacker News app. Not "essential" by any means but it's quite good.
Edit: added prognoza and olauncher
I use Retro Music. What advantages would Symphony have?