I have played it on and off for years. Once I get into a run, i play it out, but otherwise it's easy to put down, forget about for a while. Great entertainment without the addiction
Vampire Survivors: Practically an idle game. All you do in this is control your hero's movement around a sea of monsters and your hero automatically attacks them. Surprisingly fun and strategically deep. Battery killer
Slay the Spire: card collecting strategy game
Bloons TD 6 (requires Netflix): Pop Bloons with monkeys. Battery killer
Into the Breach (requires Netflix): isometric strategy game from the same devs as FTL: Faster Than Light. Big emphasis on using near-perfect information to solve tactical fights like they are puzzles.
Puzzle games:
Any of the variant Sudoku apps from "Studio Goya" on the Play store. These are the official apps of the Cracking the Cryptic YouTube channel. Handcrafted puzzles tend to have a very interesting solution path that requires you to develop logic skills.
The Room. Play as Tommy Wiseau as he uncovers an Eldritch mystery by opening puzzle boxes. Very satisfying animations, neat story
Cultist Simulator. Honestly idk what to call this one but "puzzle game" kind of fits. This is a really fun game but requires a while to get a hang of. In fact the fun of the game is learning the game mechanics, since nothing is explained except through cryptic hints and riddles. The writing is incredible but you will probably lose a lot as you get the hang of it.
Other stuff:
Eternal Card Game: I'll be honest, I haven't played this in ages, but I remember it being a better MTG clone than MTG arena. The mechanics are almost the exact same feeling as MTG, but more adapted to the digital medium. Has some pay-to-win mechanics and microtransactions but honestly the pricing felt pretty fair to me and it's not super in-your-face with it.
RCT Classic: Rollercoaster Tycoon 2 mobile port. It's not as good as OpenRCT, but it's still a lot of fun.
OpenTTD: Transport tycoon deluxe mobile port.
Papers Please: Glory to Arstotzka!
Townscaper: not really a game as much as an arts and crafts kit. You get a tile-based map and wherever you click it fills in a tile. Depending on how you fill in those tiles, they look like different little buildings, gardens, etc. really cute game with no stakes.
Mindustry: minimalist Factorio clone. Controls can be challenging on mobile but it's still fun
Maybe it's not the case anymore. Bloons and Into the Breach were ported through Netflix's game publishing thing. Maybe they opened it up at some point.
Slice & Dice is the best game I've ever gotten on my phone, I bought it over Thanksgiving in 2021 and haven't stopped playing it since. It's similar to deck builders, but dice based.
It's $7 on mobile, but has a good free to try demo. So you can see if you like it for free. It's also available on Steam and itch.io
The game is still in active development, but the dev only releases updates every 1-1.5 years. The updates are absolutely massive though and add a ton of content.
If you're into Pokemon and have access to the GBA/DS ROMs, PokeMMO is a great emulator that adds online MMO features to the first 5 generations of Pokemon. You can take one character across all 5 regions, and there's tons of QoL features.
Dawncaster is excellent. I was amazed at how deep the game is for a mobile deck builder.
It also uses an expansion based monetization rather than micro transactions and the expansions absolutely aren't necessary to get a lot of enjoyment out of the game.
I really liked Dawncaster but then I didn't play it for awhile and when I came back it had changed significantly and all the builds that I used to win with consistently no longer worked out. Honestly it's probably more balanced now than before but I haven't spent enough time with it to get good again.
Honestly I’m just bad at it so I rarely finish a run regardless. But it’s fun at least, and I bought the expansions mostly to encourage the business model.
AM2R a.k.a. Another Metroid 2 Remake
It's a fan game of the 2nd Metroid game, and is considered one of the best of the series, even though it's not an official release. It's more like Super Metroid than the Gameboy title is. You'll have to search around a bit due to Nintendo's D&C, but it's not hard to find (the internet archive has recent versions).
Minecraft
It's a good port, but probably best played with a gamepad &| tablet.
Portal Knights
A minecraft-like voxel game with more satisfying progression and combat, but less creative freedom. Plays well on newish devices, epsecially with lower-quality settings.
Terraria
It's a great game all-around, but harder to play on mobile than PC.
Emulation
This goes without saying if you like retro gaming. The best emulators I've found are the .emu apps by Robert Broglia. They can be bought from the play store, or obtained for free at his Github page. If you like original Playstation games, get the Duckstation emulator (produced by another dev.).
If you like twitchy reflex killers, two oldies-but-goodies from Terry Cavanaugh: Super Hexagon and VVVVVV.
Fun chiptune soundtracks, minimal graphics, and so much "I died already? Okay just ONE MORE try and then I really need to get some work done. ARGH - okay maybe ONE MORE try...." And when you finally succeed the dopamine is second to none.
If you have a rooted phone, an older android version, or the ability to access the android/data folder to move files around, I hear some pvz2 mods are pretty good. Only ones I can personally say are good are Refloureshed and Eclise, though it's been a long time since I've played Eclise. Both are harder versions of vanilla.
Alto - very calming and engaging game where you go down a mountain on your snowboard trying to catch llamas and do aerial tricks. Excellent vibes, no bothersome ads or micro transactions i think.
Sky Wings is pretty fun. It's super arcadey, has different ships with different abilities and shooting styles, different modes and difficulties. I've put in quite a few hours over the years.
The Flow Free puzzle games are pretty fun imo. I have most of the different ones installed on my phone, and some years back I actually bought a bunch of the expansions for the base version so I have a ton of puzzles to go through.
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
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.
I've been playing half life using xash3D for this very reason. People are on multiplayer all the time, counter strike has players too. I'm really hoping to find people playing team fortress sometime.
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.
For some ungodly reason CA also ported Rome and Medieval 2 Total War - these are certainly not the best UIs ever, but it's pretty hilarious to see how far you can push the hardware.
My favorite is Time Surfer. The core mechanic is basically the same as Tiny Wings, but the theme, artwork, levels, etc are all very different. I especially enjoy the chiptunes!
I got really hooked on Armory and Machine, there is an A&M2 but I've never played it.
Its the kind of game that only has a mobile version, it rewards you for coming back to it like any bad mobile game, but there are no ads, nothing to buy, and I don't think there is any data shared.
The premis is you are work on a machine, making it faster, better stronger, more automated, and more able to produce things. Things can be in turn, turned into items that let you travel and fight critters. The loot from the critters can be used to make your machine faster. Its all a vicious factorio-like loop, and show how fun these mobile mechanics can be when there is no company taking advantage of you.
Other's have suggested emulating Pokémon. However, if you want a native RPG, the first six Final Fantasy games were remastered for mobile. That's five whole good games! They all have very frequent auto saving, so they're pretty easy to just pick up and put down.
These aren't arcade-y, though. Others have already suggested the best. I like Super Hexagon the most of the suggestions due to its simplicity. Geometry Dash is also great, but sometimes, it just isn't sightreadable.
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
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.
It's not an arcade-style game by any means, but I can't recommend "Sky: Children of the Light" enough! My partner and I have been playing it daily for over 4 years and still can't get enough of it.
It's hard to give it a proper description. It has a beautiful storyline with new seasonal stories that come out every 3 months or so. You play as a child of light whose mission is to banish darkness and shepherd spirits from a post-apocalyptic land into the stars. However, the real core of the game is the social aspect.
It's mmo-adjacent (typical server sizes are 8 players) with other players showing up as other children of light. You slowly make friendships using in-game currency and gifting each other friendship levels. You cannot chat with others at first and must communicate through a variety of emotes until you unlock chat in the friendship tree. The way communication and friendship is handled in the game makes it one of the most friendly and least toxic communities that I've found on the Internet.
It's also cross-play and cross-save between Android, iOS, Switch, PlayStation, and Steam.
That Sky Game
As far as puzzle games, SevenBloks is my most played game by FAR. I play on Toughness mode, and the games are pretty quick. It’s a combination of equal parts strategy and luck.
For sports games, Retro Bowl & Retro Bowl College (American football) are the best $1 per game I’ve ever spent. I’ve lost track of the number of seasons I’ve played on both.