I think it’s important to support hard working mobile devs that are trying to make and sell quality games. Often great games get lost in the shuffle of knockoff, or even exploitative, mobile games.
I want to learn about some great mobile games/devs we should be supporting!
I haven’t kept up with mobile gaming in a long long time, but one game that’s been a mainstay on my device is Terry Cavanagh’s Super Hexagon. The mobile port of VVVVVV is a great choice as well.
Not too long ago I picked up Downwell from Moppin and Devolver. It was made for mobile, but personally, I think it plays a lot better on a PC/controller than on a touch screen.
And this game is Android only, but I recently ran into Daniel Linssen’s BREAKER a couple months ago. Its a odd little combo of Breakout and shoot-em-ups that took me a little bit to grasp (despite being the exact same control method as Super Hexagon) but it’s pretty engaging when you get the hang of it.
Dante Must Die Mode: The game also can’t have wide releases on consoles, handheld, or PC/Mac/Linux.
The Hitman game is pretty good, as is Lara Croft
Gorgoa is beautiful.
Dont miss Cytus II, it’s a pretty perfect rhythm game
My others are Holedown, Lumines and Reigns
These are some very obvious picks, buuut
Monument Valley 1 & 2
80 Days
Sorcery 1, 2, 3 and probably 4 but i haven’t played it
The Room
Hitman Go¹
Slightly Less Known
Calculords
Desert Golfing
Attack the Light (a Steven Universe RPG)²
Michael Brough’s games are a really neat subgenre of tactics-based roguelikes. Cinco Paus and 868-Hack I think are iOS-only (although Cinco Paus is on itch and 868-Hack is on Steam which is where I played them). There’s also Imbroglio which doesn’t have a non-iOS release as far as I know, so I’ve not played it but it’s probably still great too.
Hoplite is also great and probably the mobile game I’ve put the most time into.
There are a bunch of good paid mobile versions of board games: Carcassone, Tsuro, Galaxy Trucker, Potion Explosion, Splendor.
I am also a big fan of Ridiculous Fishing. The Reigns games are also pretty good.
Florence is great. Flower has a good mobile version.
So I guess it depends on how we count microtransactions, but I love the Carcassonne app. It does have paid expansions, but these mirror the actual board game expansions so they’re more like genuine DLC.
Others have already mentioned great options, but some that haven’t been listed yet:
Desert Golf
Solitairica
Phoenix Wright Ace Attorney Trilogy
Ghost Trick: Phantom Detective
Both Alto games! Fun little snowboarder games. Golf Peaks is good as well. and The Last Door.
Love the Alto games! These are some fantastic recommendations 
Also! I had no idea Itch had mobile games. Really cool!
Wait what!? For real?!
Totally! For instance, the game Breaker that was suggested earlier: https://managore.itch.io/breaker
Yeah you can definitely download apk files to install on Android:
Though note some of them just contain a link to the play store. You need to look for ones with the actual android icon, as that means they have a downloadable apk:
Oh my god a new world has opened up for me and I cant thank you all enough thanks folks @SuperBiasedGary
Well I was going to say Roller Coaster Tycoon but Atari pulled the original and re-uploaded to try and get people to rebuy it soooooo
Great game and at $5 it is a steal. It is the original 2 games and isn’t watered down at all they just made it work really well on mobile
Race the Sun is one of my all-time favorites, and while most of my time on it was in its PC version, the mobile version is just as good.
Hungry Cat Picross – while neither microtransaction free or technically picross – is one of my favorite mobile games. I upgraded my phone a few months ago, and the first thing I did was make sure my progress transferred over. You can pay $5 to get rid of its ads, and anything you can pay for is mostly just cosmetics you’d get through play anyway. But most importantly, I have lost hundreds of hours making my way through its seemingly never-ending amount of puzzles. You’ve got self-contained pictures to solve, weekly 3x3 puzzles (as well as the game’s entire backlog of them), and enormous 40-tile ‘frescoes’ that will take you hours to solve. It’s really one of the best deals for a F2P game I’ve ever come across.
I’ll also second Cytus II as a great mobile rhythm game. The gameplay is really fun and straightforward, and the music is extremely well curated. If you wanted to play all of it, it’s going to be pretty expensive (since every additional character is $10 retail), but if you’re cool with what’s in the base version (four characters, each with their own collections of ~12-15 songs), then you really can’t go wrong. What’s more is that the whole game is centered around this surprisingly decent cyberpunk narrative about twitch streamers getting mind hacked, and every new character you get builds onto that story.
Most recently I took the plunge and got Final Fantasy Tactics to play on my phone. And it’s Final Fantasy Tactics…just on a phone. I’m surprised how well it translates, even if it’s not a full-on adaptation for touch screens. Plus it’s just a really nice game to have when you’re out and about, and you just want to optimize your team or grind out a random battle really quick.
Cytus 2 is extremely good and (surprisingly, imo) tells a really cool cyberpunk story. Also they added Hatsune Miku DLC a little bit ago so 
Desert Golfing was also a really good meditation tool for me for a while. Theres literally no stakes in that game so it really helped me to decompress when I was really stressed out. I think I played something like 3000 holes lol
Card Crawl - Card game where you need to use the cards dealt each turn to survive and gain points. Free, no microtransactions.
Card Thief - Navigate a little thief person on a grid of i think 3x3 to steal as much as possible without getting got by the cops. good art, very simple but deep rules. Free, no microtransactions.
Candies 'n Curses - Run-based platformy thing. Kill a bunch of ghosts, fight a boss, eat a candy (powerup) or a curse (powerup, but with a tradeoff), it’s fun. Flick-based controls can sometimes do unexpected things but otherwise great game. Free with optional ads or a one-time purchase.
Meteorfall - Class based card roguelike, probably as close to Slay the Spire as a mobile game gets. Art style is a bit too Rick and Morty but otherwise it’s very good. Paid game.
Hoplite - Hex-based roguelike and probably the best one on the platform, definitely get this if you like games. Free, with optional purchase for extra levels.
