Asklemmy

Just passing by to say that with a little fiddling, you can get Morrowind running on your phone, touch screen controls and all if you don't have a gamepad.

• Another vote for "Slay the Spire", have bought it for all platforms and wasted too much of my time
• Horizon Chase Turbo is a very good arcade racer
• Danmaku Unlimited 2 and Danmaku Unlimited 3 for bullet hell shmups

Not arcade style, but Final Fantasy I-VI pixel remasters are IMHO great on phones.

Super Auto Pets is one I like

There are plenty of puzzle-style ones like Sagadoku/Blockudoku, Minesweeper, etc.

My favorite mobile games are

Don't starve

Dead Cells

Emulating old RPG games through Delta or Lemuroid

I just want to kill some time

Pokemon sleep and take a nap

Puzzler / slight programming vibe: BaBa is you

Retro Bowl - 1980s style american football game

I Love Hue, both 1 and 2

Peglin is super fun. It's wood-described as a peggle rouglike

Fancade is also great. It's an open engine for little arcade games, so there's always something new to play. There's different modes like an adventure mode and a battle mode. There are IAP's but they're purely optional and very unnecessary.

All games I'm going to mention aren't sending me any notifications.

Square on top is a bit like jump king, and let's you disable 'unwanted' Ads. You're still able to watch ads for your own gain, but dont have to.

Divineko is a fun shape drawing/reaction game that has very fair ad placements IMO.

Xeonjia is an ice puzzle game (you walk in one direction until you hit a rock) that reminds me a bit of Pokémon with its art style. I dont think it has any ads.

Those three are my go to's currently.

Twenty is my go-to. Blockus clones are fun too, and there are a lot of game modes.

This Ars article turned me on to it. Maybe click through some of his other suggestions-

https://arstechnica.com/gaming/2015/05/why-twenty-is-my-latest-mobile-gaming-obsession/

Download TIC-80 is a fantasy console that also has an android app.

Inside it you'll have access to tons of games made for that console.

I've been some weeks playing "Shadow over the twelve lands" on android TIC-80 and it has been a great experience.

It's all open source too!

You could get some minigame type games from fdroid. I have a tetris game and a 2048 game from fdroid. There's also Super Tux Kart if you want something 3D

Hill Clim Racer has been a long time favorite. Still works great in airplane mode and well.

Little Inferno

Tyrian. 90's scrolling shooter ported over and mostly functional.

I’m on iOS and actually pay for Apple Arcade. It’s been worth it. I don’t bother looking anywhere else for mobile games anymore.

Geometry Dash

here is some variety:

Brawlhalla is legit, Shell Shockers is funny, agar.io is simple but dope

You didn’t say what OS you were running, but if you’re running an iPhone, the original Sonic is in the App Store and is pretty playable on a phone. I also really liked Temple Run.

Survivor.io is actually amazing and doesn't panhandle your for money

Bloons TD6 is great and will melt your life away

Pawnbarian is a good twist on chess

https://play.google.com/store/apps/details?id=com.Level5.LT1REU

https://play.google.com/store/apps/dev?id=5341269538359321555

https://play.google.com/store/apps/details?id=com.square_enix.android_googleplay.chrono

https://play.google.com/store/apps/details?id=com.playdigious.evoland2

Lapse and Lapse 2 - clones of the Reigns game

Plague inc

Spirit Island and Star Traders

Tetris. Pac-Man 256. Brick Breaker Quest. for Tetris at least you'll want to make sure that you've got an adblock DNS set up because it's full of ads otherwise