Here are some that I've played:
Shattered Pixel Dungeon - Roguelike
Endless Sky - SpaceSim
Simon Tatham's Puzzle Collection - Puzzles
Katawa Shoujo - Visual Novel
Snoot Game - Ditto
Gurgle - Worldle clone
TuxKart - Mario Kart clone
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Here are some that I've played:
Shattered Pixel Dungeon - Roguelike
Endless Sky - SpaceSim
Simon Tatham's Puzzle Collection - Puzzles
Katawa Shoujo - Visual Novel
Snoot Game - Ditto
Gurgle - Worldle clone
TuxKart - Mario Kart clone
There's a free mobile game called sky that I'd highly recommend, it's extremely calming but also very well made.
If you like incremental games, the Kittens Game by bloodrizer is awesome. Free website, or like a 3 dollars one time payment for the app.
Solomon's Keep and Solomon's Boneyard.
Keep is a traditional dungeon crawler and Boneyard is an endless wave survival game.
Amazing brick
Atomas was mentioned in another comment; I can vouch for it as well.
A Dark Room is a fun (if not somewhat short) text-based game.
Bonza and Smash Hit are good for passing the time.
Vector Classic and Shadow Fight 2 (Special Edition) used to be my favorites as a teen, though I otherwise wouldn't recommend Nekki games since they're full of ads and dark patterns.
One thing I don't see people mentioning is that Netflix has a bunch of good games for "free" if you already subscribe.
Night of the Full Moon Clickpocalypse Atomas Rusted Warfare Luck be a Landlord Magnet Balls 2
If you like basic racing games, mad skills mx 3 is pretty fun once you get the hang of it. Straight rhythm tracks, find the fastest line and set the fastest time to compete with everyone.
Orna, it's a gps game like pokemon go but it's a standard kill monsters get loot mmoRPG.
It does have MTX, but I've never bought any and I'm still enjoying myself. It doesn't significantly limit you for not spending like some games.
I had a lot of fun with Cat Quest. Monument Valley is pretty good too. Go series based on famous video games are also fun puzzles. Start with Hitman Go, then Lara Croft Go, then I lost interes at Deus Ex Go, I don't know if they made more.
I love cat quest, can also recommend the 3 Games for 2 player couch coop with low stakes on PC!
CrossMe is great, simple mechanic and hundreds of puzzles to solve.
Backpack brawl
I play a game called townsfolk that's pretty fun but it's free for the basic stuff but a one time purchase unlocks a bunch of content.
I liked Knights of pen and paper 2, and Hoplite.
But that's about it 🫤
Through the ages has expansions and zero other mtx. Super balanced gameplay with pass and play if you need it.
I used to like Bejeweled 2, Asphalt 6 and Kingdom Rush.
Stardew Valley, which is an amazing harvest moon like game, and subnautica if your device is compatible.
Another good option is to download winlator from the internet and use it to play older Windows games. I play FTL on it. You could also play stuff like Civ probably. I think civ 5 has a touchscreen mode.
In my experience the play store is awful to use if you're looking for anything that's not full of ads and/or extremely monetized. I recommend only using it when you know exactly which app you're looking for.
Generally I find games through itch.io and recommendations from others. Also there are foss game emulators on GitHub and similar sites.
Netflix recently started offering mobile games as well.
Ages ago humble bundle did android games but that's all in the past now.
I've been enjoying worldbox and lichess. I used to have a bunch more but the latest Android version made most of my collection stop working.
Unnamed space idle: free idle game without any ads kr necessary purchases
Unnamed space idle
Antimatter Dimensions