Android

Frustratingly, these lists keep going out of date, because apps are marked as incompatible with new devices unless they're constantly updated. So I have a limited number of recommendations. E.g. the game Trainyard was terrific, but it looks like you can't get it anymore. Auro and Glyder 2 were also excellent. And Trap! was great on the original G1.

Some of these games also do have in-app purchases, but they'll be strictly "you pay X money for Y more levels" deals, which is basically fine in my book. No currencies, no gatchapon, no "pay or wait" mechanics.

10000000 and You Must Build A Boat are fun match-3 games. No in-app purchases.

The Room 1, 2, and 3 are all escape-room games.

If you liked doing constructions in geometry, the games Euclidea and Pythagorea are both good.

Puzzle Retreat by The Voxel Agents is, well, a puzzle game. Pretty fun, good slow difficulty ramp.

The Quell games (Quell, Quell Reflect) are a bit like Puzzle Retreat, but I didn't find they had as much variety. I got a little bored with them. They're quite polished though.

Star Realms is a two-player card game with deck drafting mechanics, sort of like a cross between Dominion and Magic. It's available as an actual physical deck game, but also as a decent android game with both multiplayer and a single-player campaign. Since it's a drafting game (i.e. you both recruit from the same deck), buying card expansions just changes what mechanics are available to both players, so it's never pay-to-win. I'm very fond of it.

Freitag is a single-player deck-drafting game. The android app isn't the best thing ever but it works. It's based on Robinson Crusoe.

Spaceplan is an increment game, a bit like Cookie Clicker or Clicker Heroes, but it's got a plot and an ending and is over in a couple of days. Plus it's really silly. Recommended.

Super Hexagon is a very brief action game. Only uses the edge of the screen as its two buttons, so it basically works despite the touch screen. It's only got...I think it's twelve levels total? I forget. I think I've gotten to level four. It's better with the sound on, though.

Slay the Spire is another great deck building game. Touch controls aren't perfect and the UI is kinda small on a phone, but the underlying game is good enough that it's worth playing.

Ridiculous Fishing is a very simple game, but very well made.

Pinball Arcade is pretty good, though you have to pay for each individual table you want. There are always some free ones on any given day though. It was easier to recommend before they lost their Williams and Bally licenses, since then they had all the classics like Theater of Magic and Attack from Mars; now it's all Stern tables unless you already own the old ones. The simulation quality is pretty good, though. It's all a bit more forgiving than the real thing, but I don't think that's entirely a bad thing.

Bart Bonte's games, which are all named after colors (black, blue, green, etc.) are pretty amusing. Not very difficult but kinda diverting for a bit. Kind of like an escape room game crossed with warioware? Each screen has unique touch-screen mechanics, and you have to figure them out to advance.

SetMania is a decent implementation of the card game Set. Make sure to turn off the (frankly bizarre) setting that randomizes your settings constantly.

Nonograms Katana is a pretty good nonogram (picross) game. Gotta buy levels though.

Monument Valley and 2 are kinda fun. Easy puzzles but diverting, with nice graphics.

If you find it fun to make fine distinctions between colors, I Love Hue is interesting. But I can also see other folks thinking that's a circle of hell.

Oh, and I'm enjoying Cryptic Crossword by Teazel Inc. They're not very difficult ones, and it would be nice if it had some kind of "explain" option for when you really can't grok a clue even after seeing the answer. But you usually get an "aha" from most clues and the packs of puzzles aren't too pricey.

There are a few more games I enjoyed, but that was at least partly because I got them from a Humble Bundle, and those versions had the in-app purchases turned into things you could earn in the game, which was way better. E.g. the Kingdom Rush games. I can't really recommend the versions you can get now, because they're all microtransactioned up. I think the same is true of some of the games I used to enjoy like Cut The Rope as well.

Emulation is also a good option, but if you don't want to bother with that there are a few purchasable apps that will basically do it for you, like Sega's Shining Force games.

Hope this helps someone. I wrote it up partly to get myself to organize the things in my own brain.