Tasker. One of the best Android investments I ever made. EvolveSMS (in-app purchases for themes, etc.), which my favorite SMS app. The dev's Material Design apps are top-notch.
As far as games, I can only say beyond what's been mentioned here is Knights of Pen and Paper +1, which is a great RPG.
PlayerPro is another great music player. I've been using it for years, still the best in my opinion. 10000000 is a weird but really addicting and fun game to play. Zooper Widget Pro is probably the best widget maker - thousands of pre-made themes and highly customizable. The Walking Dead Assault is pretty good - very nice comic book art style with some unlockable artwork. XCOM Enemy Within, which as far as I can tell is a full, not some crappy mobile port. I haven't played Enemy Withing on Android, but I do have Enemy Unknown (their previous-original game) on my Nexus 7.
Granny Smith was a really fun game for me, lasted a couple of hours, and was pretty cheap when I bought it.
I recently bought Machinarium (I think is how it is spelt) and although I haven't play it much, it is a beautiful game. The art work is the best on any android game I've seen, and it has pretty high reviews on the Play Store.
MC:PE is . . . meh. I'm a pretty big Minecraft fan, but the controls on pocket edition just turn me off and I try my best to avoid the game, even though I purchased it.
Reddit is Fun: I love this app. If you've never used Reddit before, well, I don't know what to say. Before you buy the premium version of Reddit is Fun, try the free version with ads.
I'm not sure if you're looking for a game or an app, but as an app I have one suggestion, "Tasker." I believe this makes an android device, an android device. It gives you almost endless automation capabilities with your phone. Such as, when I get home my phone say "Welcome home Tyler, the time is %time and your battery level is at %battery %" and it unlocks my phone so I dont have to keep on unlocking it while at home I just swipe. There is also plugins you can get to interact with other things such as a pebble, vera, chromecast, etc.