Slay the Spire is excellent on mobile, it’s a roguelike deck builder.
A lot of really good older games have been ported to mobile and work fantastically. Knights of the Old Republic, Neverwinter Nights, and Baldur’s Gate just to name a few. Hell, you can play Baldur’s Gate multiplayer, cross-platform with PC players even! There’s also fo2.exe on the Play Store, which lets you play Fallout 1 & 2 on mobile provided you have access to the files from the PC versions. Oh, and Doom ports galore, of course.
As far as mobile-only or mobile-specific games, my favorite is probably Caves, a surprisingly well done and completely free roguelike.
On iOS, there’s an AltStore app called PojavLauncher. It’s a launcher for Minecraft Java Edition, which is pretty awesome.
I also quite like the original Angry Birds (now called “Red’s First Flight”), but that’s £0.99.
On Android, have a look at the games category on F-Droid.
Definitely the mobile version of Stardew Valley
RCT classic is pretty good. Not as good as OpenRCT but still quite good.
Slay The Spire is also very good, though the mobile version is a bit bigger than the PC game
Cytus II, it’s a great rhythm game with a cool storyline
Might not be the answer you expect, but I have an iPhone and I got myself an Apple Arcade subscription without expecting much (I didn’t play mobile games at all before that, because they tend to feel either unoriginal, or scammy, or both), and I was surprised at how most games (not all games, but still) were truly original, and none of them were scammy since I was technically paying for them with the subscription. It’s been a surprisingly nice exploration.
One More Line is pretty great.
May be the commercial one but actually Candy crush is a nice one
I work at a gaming company - Candy crush is known for employing the same tactics that keep people sitting at slot machines for 8 hours a day, and every damn PM wants to copy those patterns.
