Have a folder on my iPad devoted to brain games: Have these for a start: Chess cards Really bad Chess Dice Monsters
Um... is there a specific defining factor to categorize as a brain game? Or do most puzzle games fall here? Right now i think the best puzzle games that really encourage forward thinking include Square Enix's GO series.
Have to throw in Human Resource Machine - it'll make your brain sweat. Love that game. Might as well add Paint It Back too, as picross offers great logic puzzles.