Puzzles by Simon whatshisface
https://play.google.com/store/apps/details?id=name.boyle.chris.sgtpuzzles

Bunch of puzzle games, no monetisation

Free, ad-free, open source phone games

Unciv: Civilization V clone that runs on a potato; a grand 4x strategy game. It seems pretty mechanically complete and has a lot of content. Easily modded. (Graphics may not be to everyone's taste)

Simon Tatham's portable puzzle collection: Mathematically inspired Puzzle games with a lot of customization and reasonable interface. This includes classics like untangle (graph planarity) and solo (sudoku, but generalized). I personally really enjoy Tower, and hadn't seen it elsewhere (and like 15 more games besides).

Chip defense: computer science themed tower defense. By the power of Turing, Noether, and Knuth you can strike down malicious packets attempting to corrupt your CPU. Good content, fun towers and educational bonus material, and I think it looks rather good. (Minor gripe/warning: early levels are optimally played with a lot of tapping that is not very ergonomic; this drops off after the first few levels.)

Honorable mentions (not FOSS, but still free, MTX free, and no ads beyond fishing for a rating). Higgster's game compendium: collection of games in a consistent and pleasing artstyle. Includes things like solitaire, wordle, binaro, and mastermind (20+ games total, several more have been added in the last year). This is really very well done, give it a look!

Flocks: Sliding puzzle game with excellent graphics and animations. Lots of levels, introduces new mechanics regularly, and easy to pickup or put down. I quite enjoy everything Robert has made, recommended!

Shattered Pixel Dungeon.

Infinitely replayable procedurally generated roguelike that is hard but fun to master, and a blast to play. It’s been on my phone for five years now and I still go back to it.

Totally offline, totally ad free, and still receiving active updates from the single developer.

It’s also got a pretty robust community.

Balatro and peglin

Monument valley

Balatro. Be warned though, it’s digital crack. One time payment though, no mtx

Shattered Pixel Dungeon

WorldBox

Mindustry

Unciv

A while ago, I came across a curated list of no-BS games for Android and iOS.

BS consists of ads or barriers to progress that can't be removed with a one-time payment. It has user ratings, and the highly-rated games are nearly certain to be good examples of their category.

Stardew Valley, Shattered Pixel Dungeon, Luanti with VoxelLibre, Mojo Launcher, Unciv, Lemuroid to play console games like Crash Bandicoot or Super Mario Bros, Geometry Dash (not the Lite version, that has ads), 2048, Vector Pinball, 1010! Klooni

Chess.

Hasn't gotten an update in awhile but the community is thriving.

Look for old games, that were released a long time ago before the “predation” was so required.

Osmos and World of Goo come to mind. Monument Valley 1 was a more popular, recent one in that vein.

Other than that, the FOSS and emulation recommendations here are great.

The mobile version of Papers Please is exquisite. I highly recommend reading the developer's documentary of it: https://dukope.com/devlogs/papers-please/mobile/

Atomas (Playstore)

Shattered Pixel Dungeon (Playstore) (GitHub)

Slice & Dice (Playstore)

Vector Pinball (Playstore) (GitHub)

Mindustry: an automation tower defense game

Shattered pixel dungeon: a classic Roguelike dungeon crawler

Slay the spire: a deck builder Roguelike. Probably one of the most popular in the whole Roguelike genre

Peglin: a lot like slay the spire, but plinko instead of cards

Shattered Pixel Dungeon is quite a timekiller on the phone

Hoplite

Pixel Dungeon

Tiny Folk

Unciv

Battle for Polytopia

micRogue

Doom & Dentiny

the mobile port of Chrono Trigger

and I strongly recommend the GBA and GameBoy emulators MyBoy! and MyOldboy! for playing those entire libraries on the go

Slay the spire, balatro, Ascension, melvor, plague inc, terraforming Mars, unciv, shapez...

The Room by fireproof games. Probably one of the first actual proper mobile games. Its spawned clones no IAP, no crap. Just fun, hard af puzzles.

Hoplite. Fun little iso turn based roguelike. Vampire Survivors. Reverse bullet-hell roguelike. Has spawned so, so, so many clones.. GTA:Chinatown Wars Have not played this is a very very long time, but i'm sure it still holds up (if its available). Old school (2d birds eye view) gta style.

These are games that work well without a controller, The Room actually would play worse with one. If at all.

Then of course theres emulators and roms and stuff.

The Battle of Polytopia is a fantastic turn based strategy that I've spent way too much time playing.

Beholder is also great on mobile. Similar authoritarian setting to Paper's Please, lot's of decisions, consequences and replayability.

I Love Hue is a super relaxing colour puzzle game.

A dream of mine is to make good mobile games, no ads, just a single low purchase. Realistically it just wouldn't be economically viable at all unless there is a free version with ads. But also realistically most mobile gamers aren't using a controller and touchscreens suck.

Stardew valley.

Some great suggestions in here, but I'd also like to mention This War of Mine. You can read all you like about how good and gut-wrenching it is, but I still always need to schedule some light downtime after playing it for a bit.

Endless Sky is wonderful, though the mobile version is a bit clunky (not even an "official" version afaik, but stitched on the ongoing-development FOSS game).

Steamworld Heist is so good on phones and tablets. Zero ads, dark patterns, or scummy behavior.

Balatro, all the other rougelites, monster train, slay the spire, etc.

You Must Build a Boat is an RPG/match 3 hybrid with no shady shit. Pay once. Own the game. It's pretty fun.

Walkscape is a step counter and an RPG, it's pretty cool but not exactly a game you spend a lot of time on. You mostly just walk and then check your progress and make a few decisions for your next walk (inventory, equipment, tasks, travels...)

Slay the Spire

Didn't see it here yet, but Dawncaster is a really good roguelite deck builder that was actually designed around a phone UI so doesn't feel clunky.

Uhhhh BALATRO!!!!!

if you like factory builder type games, try out mindustry or shapez

I mean... not sure if it counts as mobile but the entire history of console gaming up to few years ago works on emulators, so that's a VAST choice. Sure you might dislike 99.99% but if there is even 0.01% you enjoy, that's hundreds of games if not more!

Check https://search.f-droid.org/?q=emulator and consider a BT controller.

Scrolled the entire page. Just to not see hill climb racing, and slither.io

Hoplite - hex dungeon puzzle Spelltower - word puzzle X-COM (on a bigger screen)

Unciv

There are actual AAA full games, Feral Games is releasing a lot of their games on Mobile now (Android as example), like Alien: Isolation, XCOM 2, GRID Legends, Several Total War Entries and Tropico.

Hitman Absolution launches now in October 16th.

There are also some from other devs, like Focus' Mudrunner and Square Enix's Life Is Strange.

If you want awesome casual ones, there's Balatro, Isle of Arrows, Keep on Mining (non-slop incremental), Dungeon Clawler, Siege Up! and All Aboard! of the top of my head.

Mobile gaming is so good. There is a lot of chaff to sort through though.

• Balatro is amazing. Great to pass the time with, very playable even for people who aren't that into games.

• Slay the Spire is one of the greatest games ever made.

• Root is very good if you're into board games.

• Baba Is You if you want a mind-bending puzzle game.

• Marvel Snap if you like competitive card games, have way too much time on your hands, and hate yourself a little.

Flow free is pretty cool