You can create a Rovio account and store your scores online! This allows you to access them by signing in to your account even if you delete and re-install the game. Currently, Rovio Account is only available in Angry Birds Classic, Angry Birds Star Wars II, Angry Birds Go!, and Angry Birds Epic.
In games that do not yet feature Rovio Account, our friends at Angry Birds' Nest have also written a comprehensive tutorial for backing up your progress on various platforms. The guide also shows you how to move your progress from one device to another, as long as the two devices are running on a similar operating system. You can read the complete guide here.