• Slice & Dice
• Balatro
• Stardew Valley
• Terraria
• BloonsTD6
• Arcadium
• Shattered Pixel Dungeon
• Geometry Dash
• Mini Metro
• Brotato
• Slay the Spire
• Peglin

Old school RuneScape

I Love Hue is really peaceful

Balatro and Slay the Spire both have a lot of reply value. Very different games.

Shattered Pixel Dungeon is a really good roguelike for mobile. Ton of variety, no ads, only thing you can buy is a supporter pack that gives the ui a different fringe color, and that doesn't get pushed.

Shattered Pixel Dungeon is great, it's an open-source dungeon crawler. Neither adds, nor transactions, micro or otherwise. If you want to pay tho, there's a donation link for the dev team.

And if you still want too play GBA games, check check out the Lemuroid emulator, it's also open source and has no adds. Works for nintendoDS too.

You can find both of these on F-Droid. They're also be on Google Play, but since I've only tried the F-Droid version idk if the other has adds.

Some good ones from the fdroid app-repo.

Shattered Pixel Dungeon - already mentioned roguelike

SGT-Puzzles - already mentioned microgame puzzlers

Frozen Bubble - already mentioned bubble-shooter

Vector Pinball - already mentioned pinball

https://f-droid.org/en/packages/net.artificialworlds.boxstacker/index.html - Physics puzzler

https://f-droid.org/packages/com.simondalvai.ball2box/ - flick ball to the box for 3-stars

https://f-droid.org/packages/com.gpl.rpg.AndorsTrail/ - Massive story quest driven RPG

https://f-droid.org/packages/de.chadenas.cpudefense/ - Tower defense on a PCB

https://f-droid.org/packages/ch.logixisland.anuto/ - trad tower-defense

https://f-droid.org/packages/it.alessandropira.wesnoth114/ - hex turn-based fantasy RPG

https://f-droid.org/en/packages/org.lettucepie.flickybee/index.html - flick the bee through the course

Whatever emulator you can run and the ROMs of your choice.

Papers Please

Slay the Spire is one of my favorite games of all time, and has a nice android port I play before bed all the time. No ads, just caw caaaw

Surprised Slice & Dice hasn't been mentioned, it's amazing. That and Dawncaster.

A useful tool is DarkPattern.games, which lists dark patterns in mobile games (such as micro transactions).

Started playing Balatro on my phone at work.

Stardew Valley! It was worth the $5 already in vanilla, then it got updated with more content at no extra charge and then again. And now 1.6 is around the corner with even more. It is the love child of one dev that keeps on giving and giving and giving. And there are tons of mods of all kinds including entire world overhauls that adds even more replayability. Very much recommended.

If you enjoy puzzle games then Baba is You, Snake Bird and Railbound will keep you busy for quite a while.

Mini Metro. Its a transportation strategy game where you build and manage a city´s metro system through the style of the London tube map. You pay once and get the whole game. No ads or micro transactions.

Open Tyrian is an old shoot em up thats open source and has been ported to dozens of platforms, including android. It plays very well with touch controls.

If you want a Minecraft like game thats free and has no microtransactions I recommend Minetest (Now called Luanti). Its open source and has tons of mods.

Mindustry is basically Factorio-meets-tower-defense. It's open-source, also available on desktop.

Rollercoaster Tycoon Classic, if you feel like playing rollercoaster tycoon 1/2 on your phone. They slightly altered the UI to make it more touch friendly.

Threes

Fun puzzle game that got ripped off by 2048 and it's endless clones. They wrote a blog post on how shitty mobile game development can be.

~~Freeciv~~ Unciv on Android is an almost feature complete re-creation of Civilization 5 with minimal graphics. You can also download the JAR and run it on a desktop if you have a Java SDK installed. As a Civ player that started with 4, I found it easier to pick up than freeciv which is trying to replicate something more like Civ2.

Edit: provide correct name

Slay The Spire

I didn't see Unciv recommended yet, it's a decent mobile open source version of Civilization.

Pocket City 2 also gets a shout-out, it's not very deep but a nice casual city builder with a one time purchase.

Into The Breach

Balatro

Plague Inc - control a plague and try to kill all humans on earth (tactical simulation)

Interstellar Pilot and Interstellar Pilot 2 - human explorers jumped through a wormhole to distant space and lost contact with earth. Factions control different sectors, some are friendly some are warring. You start with a single ship and try to do anything between simple survival and building a new faction to conquer all of this new space. (Open world rpg with tactical simulation elements)

Battlecruisers - The machines won, humanity is no more. You are not the smartest robot and somehow you managed to accidentally hijack a military battlecruiser. You are pursued across the world's oceans by several navies while you try to figure out how to get out of the mess you created. (shipbuilder)

Https://lichess.org/training lets me pretend I'm improving my mind by playing.

DATA WING is a great racing game with an amazing, short story.

Turnip Boy Commits Tax Evasion is a fun little RPG with lots of humour

Dribble is a surprisingly unique platformer, free with no iaps and unique swipe controls.

You can get ports of the marble blast games on Android, I particularly like Ultra.

The Netflix version of mobile games have their micro transactions removed (or at least all the ones I've downloaded).

Endless Sky is a solid space trader and combat game, free on f-droid

Frozen Bubble is a pretty fun ~~bubble bobble~~ Puzzle Bobble clone, also on f-droid

Arx Libertatis allows you to play the full version of Arx Fatalis, a super in depth underground RPG inspired by Ultima Underworld. You need the PC game files to transfer to your phone though.