The hackers(developers) at XDA-Devs forums have already managed to root the Samsung Galaxy S4 flagship Android phone. As usual, the root is available even before the public release of the phone, similar for other popular flagship handsets.
The ROM is packaged with ROOT&Busybox into an image that can be flashed via Odin. However, the root is currently only available on the rare Exynos 5 Octa core version of the handset which won’t be available anytime soon. Galaxy S4 units that will be sold in the US which uses a Qualcomm Snapdragon 600 chipset will have to wait for the root that is still under development.