Hi! I’m a Game Boy collector / enthusiast / reviewer. And this question has an easy answer in my opinion…

Catrap

https://www.youtube.com/watch?v=FfV4MnGfiA4&t=284

• It’s relaxing. It’s a turn based, pure puzzle game. Like, there’s literally no action. The enemies don’t even move!
• It’s big. 100 puzzles that slowly increase in difficulty. I was able to beat them all, over time.
• It’s non-punishing. No time limits. No lives.
• No stress. Catrap was the first(?) game to feature an undo button. Try something out. Didn’t work? Just hold B to undo. You can undo all the way back to the start of the stage, as many time as you want.
• It’s simple. Up, down, left, and right to move. B to undo. I think A is introduced later to swap between characters?
• IT’S FUN. It looks good, plays good, and just feels good to jump around the stage. And completing a stage is so satisfying.

I hope you like it! 🙂

I’m going to stay retro because I’m on a retro kick right now. I’m also a big fan of chunky old-school graphics, so most of these are available in some form or another on GB, GBC, GBA, GG, or my personal favorite, NGPC.

I stuck with mostly mindless action or traversal, leaving off things with complicated puzzle solving or exploration and what to do/where to go challenge, hence things like Sonic and Mario yes but Metroid and Zelda no. That said, there’s plenty more if you’re up for some light exploration thinking. Shantae for GBC is a delightful example.

Puzzle/Tetris-like:

• Puyo Puyo/Puyo Pop/Dr. Robotnik’s Mean Bean Machine
• Magical Drop (I played this so much my brain would zen out and I’d have crushed all of my friends in a row without breaking a sweat)
• Dr. Mario
• Puzzle Bobble/Bust A Move

Mindless Action/Adventure:

• Metal Slug series
• Contra series
• Gunstar Heroes (IYKYK - if you haven’t played this before but you like Contra-type games, play the Genesis version, be blown away, then try the GG version and be impressed as hell with that too)
• Streets of Rage series (The GG ports are pretty incredible for the platform)
• Smash TV (SNES or Arcade version probably though, since retro handhelds never had the controls for it)
• T2: The Arcade Game is on Game Gear and it’s an impressive port to dink around with.
• Like, the entire shmup genre, but if you want retro portable, there are some Gradius and R-Type ports, GG Aleste/Power Strike 2 on GG, and probably a ton more on GBA.

Pure Platformer:

• Any early Mario mainline game
• Any Sonic mainline game
• Lion King or Aladdin, but these are so difficult you might want to save scum them just to brainlessly get past the brutal challenge

Sports:

• NBA Jam (I loved my dinky little GG version)

Other:

• Ms. Pac-Man and other retro arcade games/collections
• More Pinball! I don’t know any actual “normal” pinball games for retro systems that were all that great, but Sonic Spinball is awesome, plus there’s Kirby Pinball, Metroid Prime Pinball (DS), and even Pinball of the Dead.

Great question OP.

My favorite games ever are Advance Wars and Advance Wars 2 for the GBA. They are turn based strategy games so you can easily pick up, save, restore and play as needed. The entire series is great in my experience, up to the DS iterations.

Pokemon Sapphire/Emerald/Ruby/Leaf Green/Fire Red were my goto especially for grinding. From sound and memorization along you can play pokemon without looking… Or at least I could.

Zelda Oracle of Ages is another game which I found calming. Its more puzzle than combat, but there is still combat. Not goof got meeting but good for afterwards.

The GBC Harry Potter games or Prisoner of Azkaban are fun RPGs that I played before Pokemon. A fun time too, and can almost be played under a desk (don’t ask how I know)

Pokemon Mystery Dungeon, rogue like endless(ish) dungeon crawler. Amazing story, but the post game is just a grind perfect for fiddling as you are just doing the same thing for 99 levels… Until you find the boss. Better on DS with Blue rescue team, but red on GBA is a good choice.

Outside of mega man battle network, the rest of my games are platformers which don’t fit the bill

Maybe Celeste Classic? Apparently someone made a homebrew port of it to the GBA.

There’s also Final Fantasy VI, which can be played kinda with the brain “on automatic” on quite a few sections as well as having overall plenty of places to save.

And since you’ll be emulating them, if your device has save states features, Shantae for the GBC could be a good pick too. It is harder and less save-friendly than FFVI, but with save states, it should be better as a pick and play title.

And although focused on speedrunning, the impression I got from the homebrew Augury Red Code is that it is also nice if playing without having to focus too much on it.

Metal Slug 1 and X, and also Gunbird, all 3 released in the PS1, also benefit from save states to be more “pick and play”.