Here are some of my favorites on FDroid:

Atomic: This is a nice FOSS IRC client
Dimmer: FOSS alternative to f.lux
Episodes: Keep track of episodes that you've watched. Has a large database of tv shows.
Autostarts: See what autostarts at boot
Apk Extractor: Get apk files from installed apps
ApkTrack Check for updates on the Play Store

These are from the Play Store:
Boats for Voat: full-featured client for Voat
Slide for reddit: A reddit client in alpha that mimics the style of Sync for reddit. The dev plans on open sourcing it.
Reddit Offline: A reddit app that downloads preselected subreddits. You can set up a schedule for when to download.
Notes.md: A good markdown text editor with Dropbox integration
No wallpaper: replaces your wallpaper with a black screen
Simple Sticky Note Widget: It does what it says