I’m a big fan of FarmRPG. Semi-idle “numbers go up”, mostly text + static images game with a lovely community. It has zero ads and, even though it has a paid currency and some very unoptimized ways to spend it, the game is very generous with it (to the point where I’ve earned the vast majority of my currency by trading resources). It’s a bit janky, but fun.

Shattered Pixel Dungeon is free and great fun. It’s a roguelike dungeon exploration game, there are many forks of the original Pixel Dungeon but this is my favorite one. Similar to this is Hoplite, a very short (in the free version) turn-based, almost puzzle-like game where you have to get through monster-filled rooms to proceed. Lots of mechanics that you have to learn to use in order to survive.

For more strategy, seconding Polytopia, as well as Unciv (it even has mods!), which is a Civilization-like game.

For a simple but fun gameplay loop, Alto’s Adventure and Alto’s Odyssey, where you slide your way down various landscapes. The latter especially adds a lot of fun little tweaks onto the original’s formula.

I Love Hue and especially I Love Hue 2 are great “arrange the colors properly” games. Hundreds of levels, no nonsense, solid fun.

I highly recommend Opacha-mda

Simon Tatham’s Puzzles is a fantastic FOSS collection of logic puzzles. The only good mobile game, really.

Shattered Pixel Dungeon is fun

It’s not free, but Slice & Dice is the best mobile game I’ve ever played. It has a pretty large and good demo that’s worth playing by itself.

I highly recommend kingdom rush. Imo one of the best tower defense games.

@QuietStorm not sure if you’re into FPS games, but I’ve sunken obscene amounts of time into Call of Duty Mobile and haven’t paid a dime. It’s free to play, but they advertise micro transactions to you, which are easily ignored. And I’ve played it no problem on a $50 Moto e6.