I can't recommend Stardew Valley enough. It's $5, but so absolutely worth it. Especially since there are no mtx, and is still getting updates, albeit a bit behind the PC version. One of the best uses of $5 on the app store imo

Genshin Impact and Honkai Star Rails.

Genshin Impact successfully had my attention for over five hundred days. It's a regularly updated game that can be played entirely F2P, and I love that concept. Anyone who claims that you have to whale to get good at the game is wrong. You just have to play the game and ignore that some Youtubers and Twitch Streamers seem to believe that fake big numbers are the only way to improve in that game. In reality, I've watched streamers ignore that, and instead opt to play with their favorite romantic pairing or favorite character because they just enjoy the game more that way.

Honkai Star Rails seems to be a similar concept, however it faces a dilemma where it is a turn-based game and as a result the battle mechanics, so far, have to be more carefully considered. For example, I run a defense-healer-single attack-AOE attack team. So far, I tend to die if I don't do that. The gameplay is more simplistic than Genshin Impact, but the battles are stronger and tend to take longer. Bright side: because it was recently launched you get a bunch of free pulls! Yeah!

I put about 20+ hours into Monster Train on the PC/Steam Deck late last year and ended up picking it up again on iOS. It has me hooked all over again.

If you've enjoyed games like Slay the Spire in the past for deckbuilding rougelikes, it's perfect to hammer out a battle pretty quickly. The main difference is each level is like playing three battles of Slay The Spire since there are three "lanes" that the enemies move through. It has enough depth and replayability that you can go for quite some time before burning out.

Plus, you can add googly eyes to every character/minion in the game and I can't not play with that option turned on.

Chess/Lichess. Just a suggestion: There's some apps and sites that have premium features, but: Lichess has all the features for free, no ads, is open-source and great UI. :)

Shattered Pixel Dungeon is fun. And hard.

Basically if i'm playing on my iPad it's probably Slay the Spire. (Works on phone too, but i find it rather small).

Old School RuneScape

The Apple Arcade program is nice. I recently download the TMNT game from there and it is pretty fun.

I'm enjoying Diablo Immortal when I'm not at my PC to play Diablo IV. Interloper is also good if you like space combat. Terraria can be fun, too. Vampire: The Masquerade - Night Road is also a good one if you like text-based RPGs.

I just downloaded Tightrope Theatre - and it is pretty awesome rn. A classic platformer challenge, it has a hundred levels and is enjoyable

I don't think I've played anything but Marvel Snap since it came out. It's a turn based Marvel card battler, that also scratches the Hearthstone itch I get. Highly recommend!

Most of the Kairosoft games.

Since I have a Netflix sub, the Three Kingdoms version of Reigns has been pretty fun.

On Android there's a 2D clone of Civ V.

Mindustry is my go-to when I need to kill time offline. Cross compatible with pc android and iPhone on LAN I think, I haven't played multi-player in a long time. You could transfer save files as well. Originally a lite Factorio, last I played they added a new planet with different mechanics.

Mtg Arena if you like magic.

Lichess puzzle mode

Tetris is an all time favorite of mine, but im carrying an O-Droid for that. The touch screen mobile versions are ok too though.

Does Apple Arcade count? If so I’ve been playing Agent Intercept

Arknights (shout out to my kbin mag !arknights@kbin.social). It's a fun lil tower defense that you can easily pull out and grind some materials. Keep in mind that it is a gacha game, so there's definitely aggressive monetization, but it's definitely on the F2P-friendly side in terms of gacha.

Letterpress, since the launch of the iPhone, is still the best word game around if you ask me.

So simple, and yet so complex. A little bit of stratego in terms of holding real estate, but a vocabulary challenge at it’s core.

Old School Runescape. One of the best games ever made imo

Kittengame

I’m a huge HTYD fan so I’ve been regularly playing Rise of Berk everyday.

It's a bit niche, but I like Japanese mahjong (not the tile matching thing, the actual game) and have gotten hours out of an app called Kemono Mahjong. Cheap, onetime purchase w/no micro transactions and you can play against adjustable AI offline or online with others. It has plenty of guidance for new players.

Diablo impartial was fun for a few hours before you realised you needed to have a whale sized wallet to actually participate in any real content.

Dokkan battle, but keeping my attention is a overstatement. I mostly just sign in and do my daily missions.

I‘m playing „Rumble Heroes“ for some time now and I like it. It has mtx but they are truly optional. There is some grind to it after reaching about level 30 or so, but I like to do that in boring situations. Can recommend.

I really like the musical puzzle game "Okay?". Its one of the old classic app games to me, and has basically a million levels.

Im not sure if you’re into card games, but Marvel SNAP! Is my go to. It’s on Android and iOS.

Shattered Pixel Dungeon. I have another phone, this one is recent, with at least 2k games on it

Evan consistently updates Shattered Pixel Dungeon, and I fucking love his game. It's it's own version of the open source Pixel -f415-471f-9968-8e2f71c3ea3c.png)

@Evolone

On Android, but Raid Shadow Legends is fun. If you ignore the buy-this pop ups its easy to play for free. Also Magic: Arena is fun.

I do not play a lot of mobile games, but when i do, it is Marvel Snap.

I also do not usually play card games, but this one is very very easy to learn and pick up, and quite addictive once the flow starts going.

I play Fate grand order

I've been enjoying the idle game Egg Inc. It is a fairly enjoyable and free to play "numbers go up" type game. They don't force ads on the players, but they are encouraged. For the past few updates they have been removing little bits of the free to play friendly features, and increased prices on some of the premium stuff, but it's still a decent way to toss an hour or two into a day.