Shattered Pixel Dungeon for some great (truly) roguelike dungeon crawling.

+1 for Unciv, although I haven't played much yet. I really should...

Also, Balatro

Sorry if these are all super basic

Generally, the best options are ports of PC games. Things like Slay the Spire, Balatro, Mini Metro, Terraria, BaBa is You, or Stardew Valley. Not as cheap, but worth the price tag.

A couple of my favorite free options:

Unciv - Its an attempt at recreating Civ. It's got a lot of issues, such as lacking a lot of the more in-depth mechanics and having terrible world-gen, but its also free.

Vampire Survivors - a fairly simple but content-rich arcade game, reminiscent of old flash games.

Super Auto Pets - an autobattler like autochess but stripped down to its fundamentals making it easy to get in to, and easy to play in short bursts

FOSS (no ads, available on FDroid):

Puzzle games:

• Simon Tatham's Puzzle Collection
• Gurgle (Offline, infinite Wordle Dupe)

Strategy games:

• Mindustry,
• Tanks of Freedom
• Unciv (It's Civilisation V, but free)

Mindless games:

• Ricochlime

Emulator:

• RetroArch (just need the ROMs)

Free (no ads): Seedship (by John Ayliff)

Paid (no ads): Beyond the Chiron Gate (also by John Ayliff)

Oh man I love games that are just games. You pay a price, you get a game, you play the game.

On the turn based side we have Slay the Spire, Slice and Dice, and Lost in Fantaland. All kind deck builders but with pretty different combat. Great games with lots of depth. Also Kingdoms Two Crowns by Raw Fury is an incredibly good game. But a little more real time. I can say great things about all of them.

On the heavier note, fucking Subnautica has a mobile port now, which I hear is good. Of course you have Stardew Valley for a farming sim.

On the annoyingly spammy with pay to win features but still good games underneath, all the Ironhide games are good, especially the tower defense ones (Kingdom Rush)

For anyone interested: emulation works great in modern phones. Eden emulator runs Switch games and some work very well with just touchscreen controls (e.g. Into the Breach).

If you're ok with on screen controllers or with carrying around something like an 8bit Zero 2or Micro, then you could emulate a mind-blowing number of consoles and games.

Slay the Spire and Balatro is kind of the sweet spot for mobile gaming imo

Good open source (F-Droid):
Endless Sky
Unciv
Pixel Dungeon

Good Play Store:
Knights of Pen and Paper
Swords and Sandals
Sky: Children of the Light

Theres also a new mobile Kingdom Hearts game in development thats multiplayer and action combat, honestly looks sweet.

Monument Valley 1 and 2 are great puzzle games.

unciv - it's a opensource interpretation of civilaization. It's just as addictove and "one more turn" as that game

edit: geometry dash is also a classic, worth the small price

Surprised I don't see Mindustry here. It's a Factorio-like automation building and tower defence game. Open source, available on a bunch lf platforms including android.

I love Bloons TD 6. I think it's fully worth the asking price given they still consistently release updates and content

2048 is chill and addictive

Puzzles. No ads, no monetisation, just puzzle games.

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

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

There's a small strategy game called ‘Antiyoy’, with simplistic mechanics, which works for short-ish games: you can do a stint while waiting in queue or such. Iirc ‘Antiyoy Classic’ is entirely offline, while the regular one has an online mode. Both have no ads and near zero permissions, unless something changed since I last played.

You can try ‘Diplicity’ for an online strategy a-la ‘Risk’ where you bargain and do alliances with other players, until one of you wins the whole thing. There's no randomness. It's an implementation of the board game ‘Diplomacy’.

‘Hocus’ is a nice spatial puzzle with impossible geometry. Iirc it requires payment for additional levels, but has no ads.

The app ‘Fabularium’ runs text adventures, i.e. games where you type your actions and read the description of what happens. There are a myriad of such adventure games, many with novel mechanics. You'll need to download the games themselves separately, mainly from IFDb.org. ‘Fabularium’ isn't the only app that runs text adventures, but I like it and it supports more formats than some other apps do.

This list is a bit old so many games aren't supported on the latest android versions, but there are no micro transactions for any game on it. https://nobsgames.stavros.io/android/

Shattered Pixel Dungeon is a great one, Balatro is exceptional in every way, and Slay The Spire is crazy good.

Underhand Is a card game that I really liked, you have like a cult and you have to awake an old god. I liked the humor and the story and the cards.

Stranger Things: 1984 As others mentioned, it is a really solid old-school adventure "RPG", kinda vibe of A Link to the Past. Really felt like a SNES game. But as others mentioned it changed name and it seems that now you need a Netflix account to play it, before it had not restriction.

This is just a honorable mention because it is not available anymore on the play store, but The Witch's Isle was really nice, one of this point and click adventures, nice graphics and all. Not sure why it is not available, and it was free years ago, But it is on steam at least if you are curious.

I wish I had other games to recommend, but I also struggled to find good games and specially ones that are in portrait which I think would be better for casual gaming on the go.

Most every game I can think of when it comes to games, most people have already suggested. Though I haven't seen Feudal Tactics ( available on fdroid ) mentioned. The game isn't all that complex, but it can be time consuming on larger maps.

I also just looked something up and Maze Mice from TrampolineTales ( the Luck Be A Landlord dev/team(?) ) is available on the play store, if you don't mind paid apps. Cannot say what the price is in other currencies, but $4.99USD is the price I saw.

Slice and Dice. A rouge-like dungeon crawler where each party member has a unique dice that you roll to decide which ability is used each turn. You can get it on itch.io. a cross platform license is $18 but an android only license is $9.

The game has an incredible amount of depth so I highly recommend looking it up.

Hoplite for replayability

Dungeons of Dreadrock is short but a fun puzzle game

I've recently tried Peglin and enjoyed it a lot. Sounds like something you might like (a mix between the Peggle formula and deck builder)

I've been playing unciv which is a civ clone. Nice and clean. https://play.google.com/store/apps/details?id=com.unciv.app

Kingdom two crowns

Bad north

Alto's odyssey

Geoguessr :)

And i won't mention Shattered PD because everyone else did...

I've been playing Walkscape. https://walkscape.app/

In threads like this I will always recommend Swordigo. https://play.google.com/store/apps/details?id=com.touchfoo.swordigo

It's an old side scrolling platform game. The gameplay is very nicely balanced so you won't have to grind anything. There's a few difficult jumps and tactics for bosses, but the difficulty increases gradually so you have a good chance of knowing what to do when you get to it, instead of being frustrated.

It takes a few days to 100% it. I think I've done it 3-4 times by now.

Zachtronics Solitaire Collection

Ahhhh Tomb of the mask … fond memories playin that on my iPhone 4s back in the day

N E ways , (Balatro|Baba is you) pretty gꝏd mobile games

• Balatro : be prepared to stay up till dead of night . WILL (WASTE YOUR TIME|DRAIN BATTERY ON LOWER END DEVICES) so ⚠️ BE CAREFUL ⚠️ Otherwise , solid "just pick up and play" game
• Baba is you : gets pretty challenging early on but heard gꝏd things about

Dicey Dungeons is great.

Right now I'm playing Umamusume (I've been playing since the summer), which is a Japanese anime girl horse racing game. It's a gacha game, but they are pretty generous with the stuff they give out, there really isn't a need to go beyond free to play mode.

I enjoy ppsspp myself. The psp had a good collection of games that work very well as mobile games. All the Dj max games, half minute hero, cladun, disgaea, Patchwork heroes, and my personal favorite title for a game series

Holy invasion of privacy badman, what did I do to deserve this?

I replayed Grand Theft Auto Vice City on my phone a few months ago, that was a good time but it was better when I was using a Bluetooth controller

Simon Tatham's games

Xcom 2 and other good games made for PC/console that have gotten Android ports.

But if you have a SteamDeck you'd be better off just getting the PC versions.

The only game specifically made for mobile I've ever found to be good is Pixel Dungeon and specifically the Shattered fork.

The ones I have played recently are Pirate Solitaire and Vector Pinball, both available on F-Droid.

Triglav. Diablo like dungeon Crawler.

Reaper: tale of a pale swordsman

I've been going hard on Stardew Valley. Just had another kid and no good opportunities to play on PC now, so I bought a Backbone controller off of Amazon and turned my phone into a Switch.

See also: Night of the Full Moon, Card Crawl, Tiny Rails, Inotia 3 & 4 (3 isn't available anymore, but you can get an apk), Talisman: Digital Edition, Dungeon Boss: Respawned (requires Netflix sub now, but no more P2W), Survival Day R.

I'm not much of a mobile gamer, but my favorite is Lifeline. One if the few instances where it really makes use of the medium it is in.

And it's a pretty fun scifi/action/mystery story!

Vampire Survivors

Balatro

Umamusume Pretty Derby

Roller-coaster Tycoon 2 classic

MyBoy Gameboy emulators

I played a lot of Sky Force and Sky Force Reloaded. Pretty sure you have to pay to remove ads. Another single payment doubles the "stars" you earn which cuts back on the grind for upgrades. There aren't a ton of stages so a lot of the replay value comes from trying to beat stages on higher difficulty. If you're into v-scrollers it's a visually beautiful game with fun bosses and solid gameplay.

I sunk some time into Retro Bowl for a while too. Fun little football (Gridiron/American football) game with retro inspired graphics.

Truth be told that's about the extent of Android games I found enjoyable. Since getting a Steam Deck and TrimUI brick, I bounce between Factorio, OpenTTD (has an Android port but I haven't tried it), Rimworld and emulating plethora of nostalgic console games.

Edit: forgot about Mindustry and just saw it mentioned above. I'll definitely add that to my recommendations. I prefer on PC or Steam Deck but it plays well enough on Android.