Microsoft has not made any official announcement on the exact system requirements to run Windows 8, other than the general statement that the hardware requirements will be similar or lower than Windows 7 hardware requirements. Here is the official hardware requirements for Windows 7:
# 1 gigahertz (GHz) or faster 32-bit (x86) or 64-bit (x64) processor
# 1 gigabyte (GB) RAM (32-bit) or 2 GB RAM (64-bit)
# 16 GB available hard disk space (32-bit) or 20 GB (64-bit)
# DirectX 9 graphics device with WDDM 1.0 or higher driver
There is an important point to note here. Windows 8 is expected to run a wide range of devices and machines and not just desktops/laptops. The above hardware requirements to run Windows 8 may not be applicable on other devices like tablets and slates.
In general, all modern tablets and slates offer better configuration than shown above. So, if you purchased a computer/laptop/tablet/slate in last 2 years, you may not need to buy a new computer to run Windows 8.