Im surprised no one had mentioned Fallout Shelter. Its the only mobile I've played other then angry birds.

Firstly I need to agree with the posts saying shattered pixel dungeon

Second if you haven't seen anything on it look into https://www.luanti.org/en/

It is technically just a game engine but there are a bunch of games on it including one called minetest that is very similar to Minecraft

Other bonus is that the engine and thus all the games run on windows, android, Linux and I think Mac

Other fun options but they are technically ports and are technically maybe paid

1 there is software to add Mobile controls to old wolfenstein and doom games

2 you can get a gba emulator like lemudroid from f-droid and play any gba game you can get a ROM for

(Some of the ROMs can be found on archive.org for free if you look)

Simon Tathams puzzles. Its available on f-droid.

https://f-droid.org/en/packages/name.boyle.chris.sgtpuzzles/

That's a really wide question. I'll give you my list of answers.

Here are my top three:

• Shattered Pixel Dungeon, a roguelike descended from Pixel Dungeon. It's strayed quite far afield from the original PD, but I think most of the changes are good.

• Mindustry, a hybrid tower defense and systems-building game. I've heard it compared to a game called Factorio, but I've never played that, so you'll have to take it with a grain of salt. Sorry.

• Forkyz, a crossword app, which is a fork (appropriately) of a game called Shortyz. It allows you to download daily crosswords from bunches of sources for free and play them at your leisure.

• Chip Defense, a tower defense game themed around computers. It's really fun if you like computers and/or tower defense.

• Space Trader, a text-based game heavily inspired by Elite. Travel a galaxy, trade goods, blow people up, complete quests, buy a moon.

Here are some games on F-Droid that I'm not going to link, because i don't know how they do on Android, but I love them on PC:

• Luanti, which used to be called Minetest. It's an open-source voxel building game engine (like Minecraft). It's very scriptable, and you can build a lot of stuff with a little knowledge and looking at examples.

• Battle for Wesnoth, a turn-based hex-grid strategy game with day/night mechanics and multiple campaigns, both included and downloadable. And it's got multiplayer too!

• Endless Sky, a spaceflight game which borrows heavily from the Escape Velocity series. If you like the concept of Elite, you should check it out.

• OpenTTD, an open-source version of the classic Transport Tycoon Deluxe, but so much more.

Hoplite

Pixel Dungeon

Depends on what your definition of "good" and "free" is. If "free" means no money down and also no ads then I'd recommend Unciv. I think it's quite good.

What type of game are you looking for? I’ll always recommend Shattered Pixel Dungeon for turn based roguelike.

Recently became aware of Minedustry. Looks interesting.

https://mindustrygame.github.io/

Polytopia

Also some games I tend to install on every device I own are:

Crossword Puzzles by Redstone Games… good puzzles, simple Ui, minimal ads

Simon Tatham’s Puzzles by Chris Boyle… excellent port of many classic logic puzzles, no ads

250+ Solitaires by Alexei Anoshenko… many great solitaire games, minimal ads

Sword of Convallaria, it's a gacha game, but the gacha is probably least intrusive i ever seen in similar games, and it actually have entire story mode that you can play for free with barely even engaging in main mode since it have separate character pools. It's also heavily modelled after Final Fantasy Tactics and imo managed to keep the vibes and feeling better than any other similar game.

When i have 5 minutes to burn on a commute, I play chess puzzles on lichess.

Xeonjia, It's on fdroid.

For a chill puzzle game, I've been enjoying the water sort puzzle from Martin Kunze. I like that version specifically because there's no ads, no monetization, no data collection, no login, no nothing. You just sort colored water until it stops being fun.

Underhand is a nice little resource management game.

https://f-droid.org/packages/name.boyle.chris.sgtpuzzles

Legends of runeterra has a single player campaign that is probably the funnest card game ive ever played. There are in app purchases, but ive been playing off and on for about 6 years and ive never bought anything. No ads either. Rogue card adventure i think is another really good one despite the less than impressive name.

Optionally, its fully possible to get an emulator on your phone. Id recommend a bluetooth controller (a lot of older phones wont allow wired controllers even with the adapter, but ime every phone allows bluetooth controllers) but its not required. You can emulate any game from atari all the way up to gamecube on the shittiest $20 walmart phone with a screen.

Finally, as long as you are on android, technically you can get almost any app for free. Super illegal and they definitely (wont) prosecute you, so i would highly advise against checking websites like apkaward, as you might find malicious programs that install fully playable games on your device, such as the amazing star wars:knights of the old republic 2 android port that can be found on that site. Fair warning though, if you accidently end up up with kotor 2 on your phone id highly recommend getting the content restored mod. It adds back in all the cut content and fixes a slee of potentially gamebreaking bugs. On current android you do have to use a conputer to install the mod, but its very easy and i can help you with that part as it is entirely legal.

Mindustry, great open source game. Although it was so addictive I ended up deleting it. Now I don't have any games on my phone.

Open Sudoku you can download thousands of new puzzles.

I like Pirate Solitaire.

https://f-droid.org/packages/io.itch.pirate_solitaire

I don't know if I'm a good person to ask this but I still play Subway Surfers to this day

I've been playing the crap out of Block Blast! Hit 406,492 for a high score so far!

https://play.google.com/store/apps/details?id=com.block.juggle

Unciv. Basically civ V on mobile.

It's very questionable in terms of copyright, though

Melvor Idle gives a good taste with its demo. It's based on Runescape, but an idle version.