The built-in backup and restore
In setting, there is a backup and restore. It seems to suggest that application data will be backed up and restored upon re-installation of an app.
Does this actually work? My quick test seems to say no but maybe I am just not patient enough.
gTablet, DRH Jelly Bean 4.3
Kindle Fire HD 8.9, PAC-man
Moto X XT1058, AT&T 4.4
Samsung Galaxy S4 i337, AT&T, 4.3 rooted