A few I haven't seen mentioned yet:

The Last Express - the mobile version is the DotEmu version with optional hints and an ugly UI, and the art isn't as clean as the GOG version, but it's still a great game

MechaNika - a really short, but twisted and inexpensive adventure game

Zengrams - a short, but immensely rewarding puzzle game

Game Dev Story - absurdly addictive game development sim

Detective Grimoire - another short adventure game, this time with great music and a lighthearted story

Big Action Mega Fight - a surprisingly enjoyable 2D beat-em-up with simplistic, vaguely-RPG character upgrading and weaponized chickens

Devil's Attorney - a lighthearted turn-based RPG where you fight in court to help a bunch of obviously-guilty people get acquitted of bizarre crimes

I doubt that any of those require internet, but I'm not 100% sure that they don't.

I don't know a lot, I play those games:

Terraria - AWESOME
Pixel Dungeon - awesome
Plague Inc - just when I'm bored, you develop a virus
QuizUp - good for seeing how bad education nowadays is and how little young people know about the world

Forgot to mention Shadowrun Returns and Dragonfall. Though probably not great games for a phone, the text was quite small on a 7" tablet.

Kudos for making it OpenSource.
Is there a way to get the .apk without Google Store? I've never used it and never will.

Amazon for now. However I plan to integrate cloud saves using Google Drive which I have no idea if it'll work on Amazon.
Btw, what's wrong with the play store? It's pretty ok and it has great features like packing assets separately which reduces download size for updates.

I think I got it from one of the earlier Android Humble Bundles, and to me the controls weren't very good on the tablet.

In general, Humble Bundle at least used to be a good place to buy (mostly) DRM-free Android games, you'd get several for a couple of bucks. I've amassed several hundred Android games from there, I've bought none from GooglePlay.

The games are generally DRM-free in Humble Bundle ie. not requiring at least a constant internet connection, but some of them download extra data from the servers when you run the game the first time, to complete the installation (I don't consider those ones DRM-free, that's why I said "generally DRM-free"). So if you buy from HB and install a game, run it at least once to make sure it doesn't need extra data from the internets.

As for recommending only one Android game: Plants vz Zombies (I got the Android version from a Humble Bundle). The first game, not the sequel (PvZ2) which is just an aggravating free-to-play game with microtransactions.

PvZ is simple enough to play in small or big doses on a mobile device but still engaging enough to keep me interested, and the touch controls are perfect for that kind of game,

The first KOTOR is still available for free on Amazon:

http://www.amazon.com/s/ref=nb_sb_ss_c_0_18?url=search-alias%3Dbanjo-apps&field-keywords=star+wars+knights+of+the+old+republic&sprefix=star+wars+knights+%2Caps%2C255

I have two personal policies: No IAP, and (preferably) no ads.

Golly is a FOSS Game of Life simulator. Does that count? :P

WBT is Wanna-be-tempest.

The Green Wall is a game where you flick fruit at a wall.

Simon Tatham's Puzzles is a collection of <span class="bold">38</span> puzzle games ported from the PalmPC, if I recall right.

SolitaireCG is like every other Solitare collection out there, but no ads.

Sid the Snake is a Snake game, with a mild free flowing twist, made by the makers of I am Level.

Hot Death is an uno variant with special cards to screw many over.

Vector Pinball is basically no frills pinball.

Robot Finds Kitten is an old nerd thing and is basically a zen simulator.

Green Mahjong is Mahjong Solitare, but without the unneeded crap that most versions have.

Android Troper isn't a game. But it doesn't get much better than TVtropes on the go.

Retroarch is an all in one emulation solution with terrible documentation. Good luck. (Okay, it isn't that hard to use, but its development has been troubled. They suggest downloading a nightly APK.)

Droidsound-e isn't actually a game, but this is the closest I've got to Foobar2000 on the go.

I am one cheap guy.

Ittle Dew!

Everything with that "actually free" banner is a part of Amazon Underground, which means internet's required, sadly.

As a general recommendation, though, KOTOR is definitely way up there. The space shooting and swoop racing sections suck, but the game's otherwise surprisingly solid with touch controls. And you can play it with high quality graphics despite most screenshots out there being on low settings and blocky. Last I checked, internet's not required for the Google Play version, either.

There are only two games that have survived every new phone I've gotten:

Pixel Dungeon
https://play.google.com/store/apps/details?id=com.watabou.pixeldungeon&amp;hl=en

7 Little Words
https://play.google.com/store/apps/details?id=com.blueoxtech.sevenlittlewords&amp;hl=en

Pixel Dungeon is a rogue-like dungeon crawler built for mobile, which means it's simpler to play but not convoluted on a more limited device.

7 Little Words is a most basic puzzle game, where you're given a series of jumbled up letters and you have to put them in the right order to match the clues given.

Others have come and gone but I always have these on my phone. Hope you like them.

There is.
MyAppSharer can send APKs of files. If you don't want them sent but rather get the APK of them, you tap on an app and it'll show up in your internal SD. Also there's Xplore which can copy APK files from Google into your memory for future usage. There's many a program that can do this.

Never heard of it, this is actually some very helpful information, thanks.
I know, that I'm not the only one not using the Google Store (mostly F-Droid or direct downloads).

Thanks to everybody!
I ordered 32GB sdcard, after I get it I will try some from mentioned games :)
I hope I will get the card on this week :P