Lumosity is a game built for your brain. The app, available for the iPhone and iPad, offers a slew of Mensa-like tasks designed by neuroscientists that have been shown to improve memory and attention. The mini games have different focuses, including mental speed, attention, memory, and problem-solving skills. As you progress, the play gets harder, and the app keeps track of your scores, offering this data to researchers at Harvard, Stanford, and other universities who study the brain benefits of such games. [Free; itunes.com]