The list is comprised of open-source software organized in alphabetical order. You can find more about my commentary on phones on my page about hardware. Avoid apps and services you don't need on your phone (consider it an unsafe device).
Antennapod - podcast manager and player.
AnySoftKeyboard - android keyboard.
Droid-ify - a free and open-source app library.
Magic Earth - maps (alternative to Organic Maps)
Netguard - block access to the internet per application.
Simple Mobile Tools - a bundle of basic tools (*they are offered for free via F-droid*).