Will ArcGIS 10 run on Windows 8?

from ArcGIS Resource Center Blog.

Windows 8 and Windows 2012 Server are now officially supported starting at ArcGIS 10.1 SP1

and from ArcGIS 10.1 System Requirements

Windows Server 2012 Standard, and Datacenter (64-bit [EM64T]) *

Windows 8 Basic, Professional and Enterprise (32-bit and 64-bit [EM64T])*

i hope it helps you...