All games make you think in some way or other. However, some are designed to stretch your puzzle-knowhow more than others. There are games that don't lean on reactions or visuals to tell a story. Instead, they offer a conundrum to get you thinking.
I've worked with some people from the Thinky Puzzle Game movement to track down the best little games that get you thinking. "The devotees of such games have been known to smile at all sorts of diverse puzzles and conundrums. Puzzle games, platformers, number games, word games, games with or without grids, games with or without secrets. Easy games. Hard games. But keep it thinky and save your FPS games and dexterity-intensive platformers for another day."
Many of the games in this list look simple and, well, a bit basic. But that is part of the charm. The clever bit is how their design draws you in and gets you thinking. If you want more like this, you can find helpful people on the Thinky Puzzle Discord group.
This list includes 68 games from the last 22 years, with 187 likes. They come from a range of different genres and play-styles and are all good games if you want to get your brain working.