F-Droid is is a free store of Free and Open Source Software (FOSS) applications for the Android platform.
VLC for Android
VLC for Android is an Android port of the popular VLC desktop video player. VLC is free and opensource.
Adblock Plus is a free and opensource ad blocker for Android. It does not require ROOT on Android 3 or higher though it is the best way to block advertisements as ROOT allows it...
ownCloud client for Android platform.
Download offline maps (from openstreetmaps) for every region and navigate, even when there is no internet.
Offline dictionary - translation tool in your pocket. Uses data from Wiktionary to generate dictionary files that can be used offline. Use the long-press menu of a word to have y...
A Photo Manager
A free Android Gallery App to manage local photos: find, sort, view, copy, delete, send with Geotag support: set gps exif data, show in map, find via geoarea/map.