Since it seems like the thing to do this year, here are my most used Android apps. for 2013.
- Action Launcher - The Quickdrawer, Shutters and Shades make my home screen a tidy functional place
- Firefox Beta - Still my browser of choice and fantastic on Android.
- BitTorrent Sync - I moved all my cloud storage(Dropbox, U1) over this. I have more control over my data.
- Pushbullet - Push content from/to your phone/browser and to other users.
- PinDroid - Even with it's sync issues, still indispensable. I use it for long term bookmarks and "read it later".
- RadarScope - When I want to go deep weather geek.
- Solar - Slick UI(perhaps too slick), day to day weather app.
- Twidere - Open source, nice to look at and more functional than most other Twitter clients in the market.
- Untapped - Mmmmm beer.
- Tiny Tiny RSS - During the great Google Reader apocalypse, I switched back to my own self hosted feed reader.
- Keep - For quick notes and lists.
- Any.do - For getting things done.
- Cal - This was a late in the year addition. A nice replacement for the stock Google Calendar app.
- K-9 Mail - When I check my mail that isn't Gmail.
- Yaaic - I funnel all my IM/Campfire/IRC/Twitter into ZNC. This is how I access it from Android. One of the better IRC clients in the market.
- Hangouts - Still way from perfect, but at least it does SMS now.
- Spotify - Still the largest catalog and best music discovery engine around.
- Google Music - Mostly for my own local/cloud music. I am still a subscriber to "all access", but the selection of music is so poor I probably drop that soon.
- Google Play Movies & TV - My usage of this has gone way up this year with the introduction of the Chromecast.
- Ingress - I hardly play any games on Android, this is deep enough to keep me interested.
- Readmill - My goto e-reader. I feed it using Calibre and DRM free books.
Besides being able to control a few applications from Chromecast(Google Music, Netflix, Google Movies), I use my Android as a remote control quite a bit.