In no particular order, these are the apps I first install (or check on if they are already installed) on any Android device I use. I HIGHLY recommend every last one of them.
Though recently crippled with an annoying subscription model, Pushbullet is still one of the best and most important apps on Android. The initial use of the app corresponded with a browser plug-in to let you easily transfer pages between your computer and your device. Pushbullet continued to expand into even more useful use cases. You can send text messages from your computer, recieve phone notifications on your desktop, share your copy/paste clipboard among varied devices and computers, etc... Some of those features are now locked behind a subscription, but the core properties are still free.
I mentioned this in a previous post in which I talked about automation. Agent is a great easy to use automation app with very specific and deeply customizable functions. Set a time of night for your phone to go silent while you sleep, but let specific contacts get through, or provide an option for them to wake you in an emergency. Functions like this make Agent a must have app.
This widget represents my homescreen. Cronus is gorgeous, militaristic, and gives me most of the information I ever check my phone for at a glance. I also recommend the optional in-app purchase as it unlocks tons of amazing options.
Google Opinion Reawards
This app, THIS APP! Google Opinion Rewards sends surveys to your phone, very short and simple surveys which grant you Google Play Store credit. most surveys I get are literally 1 or 2 multiple choice questions which we then give me 10-30 cents of play store credit. Often times the question will be something like "which of the following stores have you recently visited" very often my answer is none of the above... then boom, 10 cents. That's it. Over time, 10 cents here or there makes buying mobile apps, music, TV episodes etc, much less painful. I even got my mom into the app. She is a teacher and occasionally buys songs to use in school activities, she has never put a dim into the google play store, but always has money to spend.
Yeah I know, its a bit of a cheat, but they all essentially do the same thing... these are my media apps, all of which can throw video to my chomecast as well, making them the primary means by which i consume television. Apps I use include Netflix (mostly for their originals or other binge-able series, Hulu (for some simulcast anime, as well as some originals, and lots of day after shows from network TV, and British imports), Crunchyroll (for most of my simulcast anime), Pocket Casts (for listening to or watching podcasts), HBO Go (for HBO content), Google Play Movies and TV (mostly sued for the tons of free pilots they give out, but also for when I do buy digital movies), and Youtube.
I was first introduced to Dropbox when I was running Operation Rainfall, when it allowed us to easily share digital assets. I use it frequently now to host our podcast shownotes, to move files between different computers, and to store important files, just in case. You can even configure the app to auto back-up every picture you take on your device, or every screenshot on your computer (a useful feature I use to get some screens on TVEnthusiast). My favorite aspect of Dropbox is the companion app on my computer, moving files between my computer and Dropbox is like dragging an icon from 1 folder to another... it is easy and feels natural.
If you have an Android device with google play services on it, you already have this app. Still the best webmail solution, GMail is easy to use on mobile, and the cornerstone of a good android experience. Your GMail account is your google account which links to every service they offer, it is how you keep your contacts your calendars, everything.
I use Facebook against my will, but Twitter, Twitter I love. I first heard of Twitter as a way to "text message the world", but the real strength of Twitter is as a news source... follow the right people and you have a steady flow of easily digestible and ultra quick updates on any subject you care about. I follow a lot of TV Showrunners, many of them tweet out information as episodes of their shows air. Concept art, behinds the scenes pictures, etc... Twitter is THE second screen experience for television. Beyond that, it is also the easiest and quickest way to reach out to people you would normally never have a chance to talk to.
A lot of people with android devices have probably never even used Google Now, but if you have an Android device with Google services, that isn't more than 5 years old, you have Google Now. So what is Now? In the easiest way to describe it could say it is Siri for Android, but it is SOOO much more. it is always listening for your "Ok Google" keyword, regardless of what you are doing on your phone, say "Ok Google" and it prompts you for more. You can then search the web or even cotnrol functions of your device by voice. But that isn't all. You can also open the Google Now page by swiping up from your home button. Doing so will present you to links and information that Google anticipates you might want... If you search for a game, Google Now will begin sending information about the game to you as it comes out, even when you don't ask for it. The service can also glance over your GMail account and bring up the QR codes for your flight if you happen to be at the airport. It is a brilliant time saving feature that is so good it might creep you out.
Google Play Music
Google Play Music is Google's app for listening to music you buy in the Play Store, but there is more to it then that, you can also upload up to 50,000 songs you have already to your google account for free, those songs are then available to you anywhere you can access your google account, and are treated like anything you bought in the play store. In addition to this, you can also listen to music for free by selecting automated playlists based on interests, like working out, or relaxing at home. Play Music will even create radio stations based on songs you listen to, so you can find more... all for free (though ad supported). You can also forgo the ads by paying $15 a month. This, which is the same rate as apple music) lets you listen to all of the music on the play store, but in addition to that, it acts as a subscription to the Youtube music service AND Youtube Red, the subscription based version of Youtube which gives you access to original content and removes ads from your regular Youtube experience. Personally I like buying my music, so I just use Play Music in the regular way, cashing in the rewards from my Google Opinion Surveys for albums.