I'm terrible with descriptions, so I'll give brief ones, and hope either someone can provide more insight to how each is like, or to try and dip your toes into them and see if you like them.
Ichi - Casual 1-button game where you control things like the rotating/appearing/disappearing of blocks with 1 button, and your goal is to get the uncontrollable ball collect all the gold pellets. You can also draw walls along your path so that you can bounce against it later. Puzzles get very brutal early on in regards to optimizing your moves to get an A rank.
Logigun - Some people like to call it a 2D portal. It definitely shares a lot of atmosphere and items, but your gun is more varied: you can also pull some items towards you, or pull yourself to objects, you can shoot switches with electricity which can open/close doors, etc. Looks simple but gets much harder than Portal 2
Rooms - The Main Building - There was a popular flash game involving collecting items and moving across screens to get to the goal, you have to move the screens around in order to achieve this. This follows a similar premise but includes different objects like ladders, teleporters that take you to the screen with a similar teleporter, teleporters that switch the room you're in with a similar teleporter (instead of teleporting you) so you may find objects with you that will provide more use.
First world is easy, but later puzzles will require some planning and foresight.
So Many Me - Possibly my GOTY. This is a puzzle platformer that gets brutal in both puzzle and platforming. Everything about this game is quality. The mechanics and usage of mechanics in order to create puzzles have been creative and varied. The aesthetic is cute and polished. The boss fights are challenging and rewarding being one of the few games I've played recently that have had worthwhile final bosses. There is an alternate section of the game that puts your ability to the test too, and I may never 100% it, it's tough.
As for the basic premise of this game, you control a slime that can collect clones along his journey. You can turn these clones into blocks to jump higher. 2 of you are enough to jump infinitely high by switching between who is the stone block, so you'd think it's easy, but the actual puzzles require more than that. You can eat fruits that let you turn your current clone into a different kind of platform instead of stone block. Red fruits turn your clone into a trampoline, blue into a rising fist, and yellow into a bright light.
You can also ride 3 different mounts that have their own puzzle potential behind them. There are also a small variety of enemies, as well as environmental objects like clouds, that are used well in puzzles
Sokoband - In case you couldn't get enough of chemistry games like SpaceChem, this game should sate your appetite. You control a certain chemical in each stage that may have a number of bonds around it. You have to connect every element to each other (in all but 1 section) making sure all bonds are used up. New mechanics open up very shortly including splitters that break bonds, strengtheners that adds another line to the bond between 2 elements and uses up 1 bond from each, and rotators that can rotate a portion of your current chemical mix so it can fit through spaces in the current puzzle's grid.
Would recommend
Strata
A small puzzle game revolving around wrapping ribbons over a grid of colours. The colour of the ribbon on the very top of a grid space should match the colour of that grid space, so you have to think carefully about what order you wrap ribbons around the grid in order to achieve this. Unfortunately, one strategy (once you discover it) will solve all puzzles, but it's a nice premise