I enjoy puzzles and games since they make us think and analyze problems. I play games like chess, sudoku, as well as word puzzles. Beyond that, games like Clue and Monopoly can be considered brain games. Why? Because you have to make decisions, plan things out in advance, and draw conclusions based on what you know (or what your goal is).
Brain games are fun, but the most important thing we do with our intelligence is apply them in the real world (or in the things we create). Although it might not seem like a brain exercise, writing can be a brain game in itself. The act of writing is creative, almost spontaneous, but when you get to the editing, so many crucial decisions have to be made. You have to decide what to cut, keep, modify, and add. I find myself thinking for hours sometimes on how to resolve a plot conflict or how to develop a story.
Brain games are definitely cool and fun, but when we manifest our intelligence in reality through the things we create and solve, that is the most rewarding thing.
Fallton Havenstonne 