And some of my favorites for my Nexus 7:
Super Hexagon - The only controls here are touching the left and right side of the screen to move the triangle and avoid the oncoming walls. It’s exceedingly simple, but extremely difficult. Some people hate it; some people love it. Keep in mind that you will suck for quite a while, but if you stick with it you may become quite proficient and last 60+ seconds.
Ridiculous Fishing - Another easy to learn, difficult to master game. The goal is to lower your line and tilt your device left and right to avoid the fish on the way down. Once you hit a fish, or get to the bottom of your line, the line will come back up and you then tilt your device to grab as many good fish as you can. Once your lure surfaces, the fish fly into the air and you shoot them out of the sky by tapping on them. You use your earnings to buy ridiculous accessories.
Organ Trail - A post zombie apocalypse version of Oregon Trail pretty much to the letter. Brilliant game.
Terraria - Okay I actually haven’t really played this one. Like Minecraft PE, I’ve had it on my device for a long while, but I’ve just never been able to get into it at all. A lot of people adore these games though, so maybe something is just wrong with me.
Jack Lumber - A wacky, lumberjack version of Fruit Ninja. Exponentially better.
Sparkle 2 - This is the best marble shooter game I’ve found for Android. I don’t think it’s quite as good as Zuma’s Revenge for iOS, but it’s still very nice.
Castle of Illusion - A well done remake of the classic 16-bit Disney platformer. I will say the controls aren’t the greatest on the touchscreen, but it’s doable. Wait until it’s on sale.
Sonic 1, 2, and CD - If you like the original 16-bit Sonic games, these versions are outstanding. They were reworked by Christian Whitehead and the engine used gives the game a proper aspect ratio as well as 60 fps, a remastered soundtrack, and some nice extras (like being able to spindash in Sonic 1, a re-implemented hidden level in Sonic 2, a time attack mode, as well as being able to play as Sonic, Sonic & Tail, Tails, or Knuckles, et cetera).
10000000 - A fantastic RPG, match-3 mix-up. I waited on this one for a long time because I’m not a huge fan of match-3 games, but this really does live up to the hype.
Shine Runner - Basically you pilot an airboat through river courses collecting money, then when you get to your destination you use your money to buy and sell various goods, then you choose another destination and do the same thing. The goal is to buy the goods when their price is low, and sell them somewhere else when the price is high. It’s not exactly a complex economic simulation, but it looks good, runs well, controls beautifully, and is really quite fun.
Bard’s Tale - The same modern reboot available on PC. It works very well on my Nexus 7, so if you’re interested, I would say it’s definitely worth the money.
Elder Sign: Omens - A board-game adaptation based on Lovecraft mythos. I have no experience with the actual board-game, but I’ve played a couple dozen rounds on here single-player and I really enjoy it.
Out There - Kind of a choose your own adventure space game. It has a lovely comic-esque aesthetic with some nice music and some amusing random events. I’ve never even come close to winning, and I doubt I will, but I don’t regret purchasing it.
Pixel Dungeon - My go-to Roguelike on Android.
Sorcery! - Like Terraria this is critically acclaimed and has a big following. Alas, I’ve never been able to get into it.
Virtua Tennis - The classic Sega-produced title. It plays very well on my tablet, though it does register my swings as “run here” more than I like. Grumble, grumble…
Plague Inc - If you somehow haven’t played this yet—you’re in control of a disease and your mission is to wipe out humanity. As your disease spreads you get evolution points that you can put into various transmission vectors, symptoms, etc, to help you control the virulence and lethality of your bug. Wonderful game.
Rayman Jungle Run / Fiesta Run - Mobile counterparts to the amazing Rayman Origin / Legends games. They share the same beautiful aesthetic, but these are pared down auto-running platformers. They’re still very nice games, though.
Swordigo - This is one of the better mobile action-adventure platformers out there for iOS or Android.
So yeah, there are a lot of great games available for Android. Hell this isn’t even half of what I have on my device at the moment, and I just deleted a bunch. Here are just a few games I have on here that I’ve barely touched which are supposedly great as well:
Gemini Rue
Machinarium
Inferno+
R-Type
Syder Arcade
Solar 2
Bardbarian
Delver
Doom & Destiny
Pen and paper RPG
QuestLord
Ravensword 2
Shadowrun
Star Traders Elite RPG
Wayward Souls
Star Command
Call of Cthulhu: The Wasted Land
I have about twenty more Android games from Humble on top of that which I haven’t even installed yet.
You can also run Quake, Quake 2, Quake 3, Return to Castle Wolfenstein, and Doom 3 natively on here as well thanks to some free source ports. I can attest to RTCW running beautifully at full 1920x1080 (though obviously touchscreen controls leave something to be desired).
And we haven’t even begun discussing the emulation possibilities…