Mule deer, white tail... anything you could hunt with a .30-30 Winchester can be hunted with a AKS/AK, chambered in 7.62x39.
In fact, on one of the gun forums I was just browsing, some guy had posted a pic of a beautiful buck he took with his SKS.
I can tell you first hand that the SKS kills more Alaska moose and probably wolf than any other rifle. It is the ultimate utility weapon, and if they made one in .308, it would be THE milita weapon of choice (but please, a better trigger!).
The above comment based on living on the Yukon with Indians for a school year.