List of recommended Android software

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List of recommended software for Android devices.

"App Stores"

• F-Droid (FOSS Repo) -- Also allows you to add other repository locations as well.
• Aptoide -- An alternative, decentralized set of repos that inspired F-Droid, for those who still want mainstream apps and timely updates without having to sign in to Google or sideload apks repeatedly. It features malware scanning and compares the app signature with that of the Google Play Store when available.

Web Browsers

• Firefox for Android
  • very similar to the desktop version in terms of its add-ons
  • FOSS and respects your freedoms
  • Syncs with the desktop version of Firefox
• Google Chrome for Android
  • Well integrated because it is made by the same people who made Android
  • Closed source, and receives many of the same privacy complaints the desktop version of Chrome does
  • Syncs with the desktop version of Chrome
• Lightning
  • FOSS
  • Follows Google's UI pattern
  • Fast
  • Uses the Webview engine integrated with the Android system, so older versions of Android may have security issues with this browser
  • The Playstore has a paid "plus" version and a free version. Plus comes with integrated, optional adblocking and Free version is limited to 10 tabs open at a time
  • The version on F-Droid is identical to the Playstore's paid version, but free of charge
• Naked Browser
  • Very minimilistic, barebones UI
  • Lists trust as the first feature in the description
  • Author is a confirmed /g/entooman.¹
  • Uses the Webview engine integrated with the Android system, so older versions of Android may have security issues with this browser

4chan Browsers

• Chant -- banned from the App store
• Chanu
• Party Van
• Clover -- can play webm, also available on F-Droid

8chan Browsers

• Exodus -- Full featured 8chan browser based on Clover

Communications

• TextSecure (SMS) -- Send encrypted messages. Can also work as a regular (insecure) messaging app for recipients that don't use TextSecure. Requires Google Play Services for OTT data messaging. Will lose encrypted SMS function shortly in v1.7.0.
• RedPhone (Encrypted phone calls) -- This only does encrypted phone calls, so it's a good phone app alongside your normal one. Requires Google Play Services.
• Xabber (XMPP and Facebook chat, among other things) -- has OTR support
• K-9 Mail (Email) -- supports OpenPGP if APG is installed
• Telegram (IM) -- a more secure WhatsApp/Viber replacement (please be aware that the server side is still proprietary, although you can still use "secret chats")

Music

• Shuttle -- Free version has ads, but apks without exist.
• PowerAMP -- Trial version, but may be worth the money for the extra features
• Google Play Music -- Your music from the Google Botnet!
• Vanilla Music -- A FOSS music player, for those with tinfoil wrapped phones
• Apollo -- FOSS, port of Cyanogenmod's default music player for other ROMs

Media Players

• VPlayer --Plays just about every file format ever made, but not recommended for girl cartoons
• MX Player --Recommended for anime, really good subtitle support (Will play MKVs!)

Privacy & Security

• Orbot -- TOR client for Android
• APG (OpenPGP)
• KeePassDroid KeePass/KeePassX compatible password manager
• AFWall+ Easy to use firewall (requires root)

Ad Blockers

• AdAway -- Blocks ads by editing host files - requires root
• AdBlock Plus -- Works as a proxy, battery hungry

File Managers

• File Manager - Comes preinstalled on CyanogenMod.
• Ghost Commander - Gives access to all files on the device. Requires root.

Misc.

• OsmAnd -- OpenStreetMap based mapping. Allows you to store detailed mapping info locally for offline access.
• PirateBox - Run a fileshare/chat wireless hotspot. Requires root.

References

¹ He has a bookmark of /g/ in on of the demo screenshots

Other Platforms

• List of recommended Windows software
• List of recommended GNU/Linux software
• List of recommended OS X software