This app was mentioned in 6 comments, with an average of 1.33 upvotes
Picross. I'm so addicted to these games. It's like a mix between sudoku and minesweeper.
This app is by far the best one on Google Play: https://play.google.com/store/apps/details?id=com.kb.nemonemo&hl=en
I've been playing it consistently for over 3 years and still haven't played through all the levels. And it's not one of those games where the levels get harder and harder as go until you get frustrated and eventually give up. I hate those games.
Long before The Witness I got hooked on (still am) the puzzle game picross. I've been playing it non-stop for like 6 years now, and nowhere close to getting bored with it. But anyways I discovered if I start a new round I get a blank canvas grid that I can easily fill in the squares by tapping on them and then removing them by tapping again. I first tried the paper cutouts method and this way was so much easier and faster.
https://play.google.com/store/apps/details?id=com.kb.nemonemo&hl=en
Nemo Picross. I've been playing since August 2013 and still haven't played through all the different games/levels. Still haven't gotten bored with it either.
https://play.google.com/store/apps/details?id=com.kb.nemonemo
Super basic but I've never managed to finish all the puzzles in NemoNemo Picross.
I like nonogram too! I like pixel puzzle from Konami, but cannot keep playing it because, believe it or not, it is not "simple" enough, with too much graphics in between gameplay. The nonogram I played most is NemoNemo Picross.
Another two simplistic games I recommend is (1) Fillomino from the same dev, and (2) the frequently recommended Simon Tatham's Puzzle