Awesome! Thank you!! That makes two recommendations for Might and Magic. I have heard that game is an absolute classic. I think it may have just bumped up to the top of my list.

Reigns:

https://www.gog.com/game/reigns

Imagine if "Tinder" was a kingdom-management simulator. Also one of the most casual games on GOG. And quite funny too.

EDIT:
And there's also a version for "Game of Thrones" in case one's a fan of the books.

Two votes for this one as well. And I have that one too. I have to check this one out as well. Thank you!

I play Wordscapes when I'm out and about or waiting for the wife or whatever. I've played a lot of word games on my phone and it's the best IMO.

For real games in quick bursts, I usually load up old SNES games through emulation.

Note that the Heroes of Might and Magic series is quite different from the Might and Magic series; Might and Magic games are RPGs (1-5 turn based, and later games let you switch between turn based and real time), while I believe the Heroes of Might and Magic games are turn-based strategy (so, suitable for your needs, but different).

By the way, it occurred to me that The Quest would also be a good choice. To get an ides of what this game is like, take Elder Scrolls, subtract some things (including all those bugs and glitches), and make it turn based, and you now have The Quest. Since it's turn based and save anywhere, this game is perfect for your situation.

I still need to get around to playing Starfox 2
I actually fired up Might and Magic and noticed that. Looking at the Heroes series now. I will check out the Quest

SNES is the king of casual. I always come back to play Super Mario RPG :)

That reminds me; https://hellofangaming.github.io/HelloMarioEngine. There's many projects/maps out there.

https://www.softendo.com/mario-games

For someone who consider themselves both an XP fan and a hardcore Mario player (not me...): https://www.youtube.com/watch?v=KhC829ztiTo

I think Torchlight 2 would make for a great game to play during breaks. You can play it super casually and still make good progress within 30 minutes play sessions. It's a Diablo-inspired action RPG. Lots of loot and lots of fun! There's even co-op!

Hello,
First, I would like to say, that I do agree only partially in the recommendation of SNES games. In recent times, I do appreciate the quicker load times and faster overall pace and progress in the older NES games. Why, you may ask?
Because many (if not the majority) of the SNES games introduced slow automatically advancing, animated scenes and lengthy text-based expositions or dialogues.
Nonetheless, many of those "classic" "mini" retro consoles for on-the-fly emulation of old games are a blast for shorter coffeebreak distractions!

On the other hand, here are some of my suggestions for short and accessible games for playing on a PC:

Since, Super Hexagon, Super Gravitron and VVVVVV are mentioned already by others, why not taking a look at the developer's game library for online play (in the browser) or download, such as:

* Tiny Heist -- a super quick pseudo-roguelike approach on the stealth/action genre:
http://terrycavanaghgames.com/tinyheist
(downloadable on itch.io):
https://terrycavanagh.itch.io/tiny-heist
or
* Naya's Quest -- an "isometric" puzzle game:
https://terrycavanaghgames.com/nayasquest/

Another coffeebreak classic for me is
* Desktop Dungeon -- although, I prefer the old alpha version:
http://www.desktopdungeons.net/media/

Speaking of coffeebreak, have you tried some of the 7-Day-Roguelike competition entries of Jeff Lait, other finalists during the past years or the so-called coffeebreak roguelikes listed, for instance, on roguebasin.com?
My favorite being:
* Vicious Orcs (by Jeff Lait):
http://www.zincland.com/7drl/orcs/
Plenty of options in different style, presentation (not all in ASCII/text-based) and gameplay available here:
http://roguebasin.roguelikedevelopment.org/index.php?title=Coffeebreak_roguelike
http://roguebasin.roguelikedevelopment.org/index.php?title=7DRL

Other recommendations of mine of more recently released games here on GOG.com include:
* Jump King -- but it can get much more frustrating than Super Hexagon!
* A Short Hike -- for a purely relaxing and charming experience.

Have fun!

Kind regards,
foxgog

Robot Finds Kitten http://www.robotfindskitten.org/
HyperRogue. https://www.roguetemple.com/z/hyper/
Anything resembling Tetris.
https://github.com/leereilly/games Various others.

Seconded! Really funny game.

Race the Sun is one of my "quick fix" games. With the Sunrise DLC it's also relaxing and meditative if you want.

A super casual turn based strategy game I like to play when I'm too tired for anything else, that can be played in short spells (you can't save during a battle, but battles don't last longer than 5-7 minutes I guess) is the Braveland series, that's on sale right now:

Braveland
and Braveland Wizard
for €1,79
and Braveland Pirate
for €2,49.

They're part of the Weekly Sale that lasts till Monday 22 June (I'm too tired to calculate at what time it ends).

Anthem, it is really nice to suit up your Jav, fly a couple of rounds, get caught in a event and return home again, sometimes with a epic weapon extra ;) yesterday i was suddenly shot out of the sky by a titan fireball, it was a while since i played so did not instantly recognize the treat, thank god it was only a youngster and my missile attack was fuly loaded so the young pup went down pretty easily

other games i do as super casual are

Death or Alive V ( sometimes only for about 10 mins )

and uhm nothing else really atm