For iOS:

Fully FOSS:

• Organic Maps - Offline Maps
• Yattee - YouTube Frontend
• BookPlayer - Audiobook Reader
• NetNewsWire - RSS Reader
• Signal - Encrypted Messaging
• Element - Matrix Client
• OrBot - Tor VPN Alternative
• Swiftfin - Jellyfin Client
• VLC - Media Player
• Metapho - Remove EXIF Data
• Privacy Blur - Blurring Photos
• Raivo - 2FA
• Firefox Focus - Web Browser
• Mastodon - Official Mastodon Client
• PixelFed - Official PixelFed Client
• Sync - Reddit App (RIP?)
• Mlem - Lemmy App (currently testing)
• KDE Connect - Airdrop Alternative
• Berty - Encrypted Messenger with Offline Capabilities

FOSS, but with a paid tier:

• KeePassium: Offline Password Manager
• Slide for Reddit - Reddit App (RIP)
• AdGuard - Content Blocker
• Bitwarden - Password Manager
• Joplin - Note App
• Podverse - Podcast App
• NextDNS - DNS Filtering
• Invoice Ninja - Invoicing Software
• SimpleLogin - Email Aliasing
• ProtonMail - Encrypted Email
• ProtonCalendar - Encrypted Calendar
• Proton Drive - Encrypted Cloud Storage (Testflight is Full)
• ProtonVPN - VPN
• Standard Notes - Encrypted Notes
• Notesnook - Encrypted Notes
• Tutanota - Encrypted Email & Calendar

Paid Only, but Open Source:

• Cryptomator - File Encryption
• ente Photos - Encrypted Photo Backup
• Mullvad VPN - VPN
• IVPN - VPN

Privacy Friendly, but not FOSS apps:

• QuickScan - Document Scanner
• Hello Weather - Weather App
• MySudo - Phone Number Aliasing
• Mobius Sync - Syncthing Client
• Privacy.com - Virtual Credit Cards

Edit: Added ente Photos, Mullvad, IVPN, Tutanota, Standard Notes, Notesnook, and Berty

Just mentioning the tools I had not seen on other posts:

Selfhosting

• https://github.com/wallabag/wallabag - Instapaper/Pocket alternative. Has mobile clients and hosted version as well
• https://github.com/paperless-ngx/paperless-ngx - Great document management system, has multiple apps by third party developers
• https://grocy.info/ - ERP for your household (food inventory, grocery list, chores) - there are multiple open source clients for it as well

Android

• https://f-droid.org/en/packages/net.osmand.plus/ - Routing based on OpenStreetmaps
• https://f-droid.org/en/packages/org.oxycblt.auxio/ - Audio player
• https://f-droid.org/en/packages/ws.xsoh.etar/ - Calendar
• https://ntfy.sh/ - Pushbullet alternative, can be selfhosted as well. Works as a - https://unifiedpush.org/users/apps/ provider.

I have neck issues and emulating my phone on screen is a must! I cant get enough of 'guiscrcpy' Open source Android screen mirroring! Multiple phone support, works perfect! https://guiscrcpy.srev.in/

https://aria2.github.io/

aria2 is a lightweight multi-protocol & multi-source command-line download utility. It supports HTTP/HTTPS, FTP, SFTP, BitTorrent and Metalink. aria2 can be manipulated via built-in JSON-RPC and XML-RPC interfaces.

Darktable is a great photo editor (similar to Lightroom).

I can't say for sure because most of my apps are FOSS, and they are all really good. I'm a KDE user so I really like KDE apps, KMail and NeoChat allows me to connect with people while being integrated into the rest of the system. I also like SoulSeek, a p2p file sharing app useful for downloading music.

If we're talking about mobile apps only then ntfy, Fluffy Chat, KDE Connect, Nextcloud, Tuta, Protonmail, Session, Conversations, Organic Maps, Fedilab, Mull, DAVx and KeePassDX.

For me would be on Android:

Seal: for downloading any video, specialty YouTube

ViMusic: For listening to music from YouTube

Paisa: for budget control

Read You: best RSS I had seen on Android

Xtra: Twitch client without the ads

Quacker: For following Twitter accounts without creating and actual account or interacting with them t all.

Most of them are on F-Droid and they use material design.

Let me know if you want direct links. And Droid-ify is the best F-Droid store client out there

hmm... i'm on macOS, so I had to go through my apps to see which are FOSS, as it's not always clear. More than I thought, so I'll list some of my favorites:

• Pulsar (a fork of the discontinued Atom) - a text and code editor
• Cyberduck - my favorite FTP client since forever
• Handbrake - swiss army knife for video encoding/transcoding
• OverSight - makes sure my webcam stays off when it should
• LuLu - watches my ports and incoming/outgoing connections
• KnockKnock - guards against processes (malware) trying to gain access to system services and resources surreptitiously
• Sonarr, Radarr, Prowlarr, Overseerr - a suite of media and download management applications for Plex Media Servers
• Transmission - a simple yet powerful bittorrent client
• Homebrew - a complete and extensible package manager for macOS, much like apt or rpm
• VirtualBox - Virtual Machine solution

and many more!