Sudoku.
I tried this yesterday, and when I finally understood the rules of how to play it, I was solving those puzzles like there was no tomorrow. I absolutely love how it requires critical thinking so it helps with making your brain exercise, therefore improving its capabilities of memorizing/learning things and whatnot.
Although some people don't find it fun, Sudoku is still a great puzzle-solving activity to complete to exercise your brain. And since I found it fun, I was attached to it for about 2 hours until I decided to give my brain a rest. Haha.