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You can now play a game on your iPhone, iPad, or iPod touch, put it down and pick it up pretty much where you left off. Game Center is now in "Mountain Lion". You can connect with your friends and share your scores on Facebook. You can also see your friend requests and other game details.
Documents in the Cloud allows you to store text documents, pictures, and other content in iCloud and access it from anywhere. No manual uploading required -- simply drag in your files to the window and they will be uploaded to iCloud automatically.
Another new app to "Mountain Lion": Reminders. It's another port-over from iOS 5 and iOS 6, allowing you to see your list of things-to-do on your Mac. It also supports location-based reminders, so you can be buzzed about something when you leave work or arrive back at home.