Pfft, I say let there be as many puzzle game threads as there can be. I just don’t want to rewrite about all of those games on account of my crippling laziness.
Since someone mentioned the Hexcells pack and the upcoming Steam sale I’d estimate is about a month away, there is also now a bundle for the entire -Cells quintology:
In terms of other mathematic/logic non-picross puzzle games, other than the -Cells games my favorite one is likely Slitherlink for the japanese DS. Basically you have a huge grid where certain squared have a number between 0 and 3 in them, which represents the numbers of sides of the square have a line going over them. When it is finished you have a complete loop that does not overlap itself. The same game is in the Simon Tatham Puzzle Collection under the name Loopy. You can find it here:
https://www.chiark.greenend.org.uk/~sgtatham/puzzles/
There’s a ton of other puzzle games of that ilk there, feel free to poke around. I would also recommend PicPic/Piku Piku for the Euro/Japanese DS and Patterna for the PC. Would recommend the demo for the latter as it has very tricky rules.
Felix mentioned English Country Tune, let me point out that while it has a demo the game has an odd difficulty curve where the second section might be the trickiest in the game for a first time player. This is due to the fact that the way gravity works in the game is relative to a tricky degree that takes a good bit for one to wrap their mind around. You can basically move on any surface and the gravity of anything you push is relative to your orientation on said surface. It eventually makes sense.
Here is my DROD Let’s Play, try not to hold my questionable LPing (especially early on) against it.