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.
Slay the Spire is excellent on mobile, it’s a roguelike deck builder.
Slay the Spire is crazy fun. And literally infinitely replayable
Definitely the mobile version of Stardew Valley
Magic the Gathering: Arena. The mechanics for getting gold, packs, and cards uses semi-toxic dailies/weeklies, but it’s do-able to play free2play.
World of tanks blitz is amazing.
So is my heroes for RPG
I think Ridiculous Fishing is one of the best mobile games ever conceived. Just a beautiful fusion of different games that’s a bunch of fun. It’s a bit old, but I have incredible memories playing it. Tim Rogers wrote a nice long-form essay about it if you care about that sort of thing.
I also play a fair bit of Super Auto Pets. I think it took the autobattler genere and distilled it to it’s essence. It’s great fun.
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.