Generally it isn't possible without rooting. This is why many newer games are starting to use Google's Cloud Save ability to help out the users with device changes.
Samsung Galaxy S® 4 MJA Rooted with CF Auto-Root Tutorial
HTC EVO Design 4G™ v4.0.3 Bootloader Unlocked & Rooted with HTC SuperTool v3
If it ain't broke, use a sledge hammer.