probably wanna give a little more detail on what type of games you like

Hmm it is a good question, I think my favs are the turn based strategy games but I like everything if it is good.
On mobile I played a lot with car games, I dunno why.... maybe because these are the most popular ones.
On my old tablet I played Fifa and Pixel Kingdom many times.

Edit:
I found this now:
https://play.google.com/store/apps/details?id=com.dotemu.anotherworld&hl=hu
Another World, I really liked it on pc many years ago :) Did anyone try it, is the pc port good?

I pretty much got into rogue-likes, especially on Android.

Pixel Dungeon is a nice one. No adds or something else.
https://play.google.com/store/apps/details?id=com.watabou.pixeldungeon&hl=en

They released the source code, so it's got a lot of mods. If you find the original too hard, you can get an "Soft" version.

Hoplite it's another one.
https://play.google.com/store/apps/details?id=com.magmafortress.hoplite&hl=en

NetHack or WazHack, depends on what interface do you like more. I like Wazhack more.
https://play.google.com/store/apps/details?id=com.wazhack.WazHack

I started to like these as they are the kind of games that work great in coffee break, you can close and return to them whenever you like to without any problems.

Then, for more "serious" sessions, you can try Square Enix classics. Chrono Trigger, Final Fantasy, Dragon Quest. If you are into RPGs, Android it's great platform for these, as you can't find them on PC.

Some shameless self promotion

Idk. i nvr played it on android.

You might wanna try Braveland & XCOM:Enemy Unknown.
Both are pretty good.

Well, a few no-internet-required I've enjoyed are:

Terraria

Monument Valley

You Must Build A Boat

GemSpinner

Knights of Pen & Paper +1

Elder Sign: Omens

Broken Sword 1 and 2 (Edit: These are really excellent ports, and work well with touchscreen.)

Don't forget that if you install DOSBox Turbo or another emulator, you can play a number of old DOS games on your Android device.

I've never used Google store and got all my Android games DRM free from Humble Bundle, so my choices may be a bit different.

My favourite Android games so far that work well without additional gaming equipment on my tablet:

EDGE Extended
Monument Valley
Splice
Badland Premium
Monsters Ate My Birthday Cake (yes, it's really good)
Tetrobot and Co.
KAMI
Odd Bot Out
Strata
Type:Rider
Sleepwalker's Journey
Machinarium
Botanicula
Monster Loves You! (Excellent interactive novel, quite unique.)
Broken Sword 1+2 - Director's Cuts
Color Sheep (It's dumb but cool)
ChuChu Rocket (Dreamcast port)
Fieldrunners 1+2 (If you're into hard Tower Defense)

I've still got a huge backlog thanks to the Humble Mobile Bundles though and may yet discover great titles.

Terraria - once you start digging there is no stopping...

Gobliiins trilogy
Fish Fillets NG

Might as well answer this one...

King Oddball - Has been playing this one in these last days, it's kind of simple approach to the whole angry birds gameplay but i've been enjoying it for what it is, especially considering that it doesn't something that i hate, gives you stars/scores for your performance, just defeat all enemies and move to the next level.

Rebuild - I've enjoyed this one, you control a group of survivors and must make some decisions about what to do, you will have to send some survivors to scout for food/weapons/another survivors and/or defend your base, there is different ways of completing the game, if i remember correctly you can leave the city, capture all the points of the city, find the cure, etc.
I just bought Rebuild 3 with the free $5 credit that you get if you download one of the Amazon Underground apps (free) so i'm looking foward to play it.

The Room 1 & 2 - Really amazing games that everyone that has a capable mobile device should play it, the touch controls works perfectly and it's one of those games that you feel (mentaly) rewarded every time that you resolve a puzzle, waiting for a sale on the 3 one (yes, i'm that cheap).

Braveland - Good turn based strategy game, a bit simplistic from those that people usually play on pc and in my case that's a plus because i hate losing a ton of troops and having to backtrack (and manage my finances) to get new troops.

CrossMe (premium) - It's really addicting, you have to complete the pictures by calculating the dots and free spaces, i never completed the game because it got really hard so i lost my interest, still it does have a lot of content (even with easy/medium puzzles).

Deep Loot - I got it from Amazon Underground apps (free), it's a roguelike (lite?) so it's one of those that you will until you get bored because there isn't any ending but until then you have fun with it by collecting the loot and upgrading your stuff.

Dungelot - Another roguelike, same as the game mentioned above, collect gold and level up your characters and see how far can you go.

TOI: Fallen Knight - This is an amazing underrated title, it's a bit of a make your own adventure mixtured with rpg elements and management (food/water/cold), it lasted something like 20 hours so that's something to consider if you want something to play for a long time.

Plants vs Zombies - A classic, i assume i don't need to say why it's worth playing. :)

10000000 - It's a good match puzzle rpg game, if i remember correctly when you die you can use the money that you got to upgrade your character so it does have that rpg/roguelike element. I think there's a sequel with a boat but i don't know anything about it besides that.

Deep Dungeons - I bought it a few weeks ago on a promotion for 0.10€, it's a good game with a bit of grinding, you have to pass some dungeons and collect gold to upgrade your character and on the way you can grab weapons and potions, the gameplay is simple but challenging, only two "buttons", attack and defend but you have to time it well.


Haven't played it but heard good things about it (and have it on my backlog)

Monument Valley
Hitman Go
80 Days
Choice of Robots
Little Inferno (played on pc and it was fun, not sure if it's a good port)
Sorcery! 1, 2 and 3.
Tiny Thief
Out There
Total War Battles
King of Dragon Pass
Autumn Dynasty


I could also mention Kairosoft games and Warhammer Quest but i do believe they have always online drm so...

Hitman GO
Seriously, one of the best puzzle games I ever played. Its not too easy, yet its also not too hard. All the goals are realistic and achievable given you put thought into them. You move Agent 47 across a predefined board with enemies and sometimes collectables on it, and you have to either go to the next level or assassinate the target, along with other side quests such as finishing some boards in less than X moves, etc.

Super Hexagon
This game is as pesky as its PC counterpart. You control a lone arrow on a hexagon shape and prevent it from being crushed by other shapes that merging into the hexagon.

Carmageddon
Yeah, this game is on Android, and its as satisfying as ever. Speaking of which...

Crazy Taxi
This one's here too.

Gunbrick
Its also a puzzle game that has you controlling a cube with one side having a gun mounted in across a 2D landscape in order to reach the end. Its a good game insofar.

Minecraft Pocket Edition
Some people say Terraria here, but Minecraft is also a choice on mobile. What I can say about Minecraft? I simply can't say enough about it.

Sonic games
Sonic games titled 1, 2, 4 Episode I, 4 Episode II and prolly Advance if you can play it are all good Sonic games. There's also Jump which is also another really good Sonic game, though it has IAPs (which you can forget about as the game in a whole uses rings as the only currency, which you can get in abundant amounts in levels).

Spoiler Alert
You'll unplay this game from the last level to the first level.

Monument Valley
Its a short but sweet puzzle game. Though it isn't really hard though.

Odd Bot Out
That's one of the best in the puzzle genre, and its 2D. You'll guide your robot out of the factory by using whatever the factory gives you. Its a nice ride.

VVVVVV
One hell of a hard game. Brace for tough end 2D action.

Ittle Dew
Love Legend of Zelda? Then you'll love Ittle Dew.

Pixel Room series
Both games are going to take your brain out of your head as you lead your protagonist to the door.

LYNE
Its a puzzle game that'll try its best to complicate your line-matching. Better be prepared for everything.

The Grand Theft Auto series
III, Vice City, San Andreas, Chinatown Wars. Pick your flavor and play.

Mickey Mouse's Castle of Illusion
Its a good platformer if you ask me, and its more forgiving than its Genesis counterpart, but still do not underestimate it!

Scribblenauts Remix
Scribble anything to achieve the goal at hand. What's not to like? You can even scribble an evil clone of Maxwell (yourself)!

Worms 2
Classic Worms gameplay is there. There's nothing not to like about it especially if you are a fan of the series.

Ending
Another puzzle game I liked. Move your block (which looks like a @) to the finish without being crushed by enemy blocks!

Virtua Tennis Challenge
That's a great tennis game from SEGA. You'd love it.

Choice of Robots
Not a game exactly (its a text adventure), but its still worthy enough. You'll be leading your protagonist through a robot-related future. You'll love it.

Now that's a decent amount of great Android games to play.

There are a lot of PC games on Android. Lots of adventure games, the Enhanced Editions of BG1/2, IWD1/2, Final Fantasy up to 6 (7 might make it one day, it's already on iOS), HoMM 3 is there, probably good for a strategy fix. The Banner Saga is there too, The Bard's Tale, KOTOR, ...

Autumn Dynasty is a native mobile strategy game which was recently featured on a Humble Bundle.

By the way, I hear that Final Fantasies from Google Play suffer from always online DRM. Is it true? It seems some reviews says that it has been removed that, and the Amazon version doesn't have an inherent always online DRM.

I'll try to remember to check it on my copy of FF4. Although according to this it works fine without an internet connection, and has for a while now.

Edit: According to this FF3 could be played offline 3 years ago.