We still have no firm release dates for the Galaxy S4 however some developers over at XDA have already managed to root the device! They have torn apart and repackaged an unreleased firmware nice and neat into an ODIN flashable image. They have also included root and busybox. This Root will work for the Exynos 5 Octa Core version of the phone. This doesn't help us much stateside as we will end up with the Snapdragon Qualcomm 600 variant. This is however very encouraging as it shows that these devices can be easily rooted. Samsung has been known in the past for being pretty hacker friendly. They comply with locking down Verizon's devices, but not so tight that developers like Adam Outler can't get in. If you are one of the lucky few to have the Exynos 5 variant of the device grab the rooted Rom from the link below!
Just wondering who is buying an S4? Let me know in the comments below.
Update: According to a few very reputable developers/exploiters this will not root the phone in and of itself. Chainfire and Jcase have both said that this won't actually root the phone, but Chainfire has said he suspects the phone will still be easily rooted when it launches and developers have the device in hand.