System Requirements - The Elder Scrolls V: Skyrim wiki

Minimum System Requirements

•  OS: Windows XP, Vista or Windows 7
•  CPU: Core 2 Duo 2.0 GHz or Althon X2 2.0 GHz
•  RAM: 3 GB
•  HDD: 15 GB
•  Graphics: 512 MB card
•  Sound Card: DirectX 9 Compatible
•  DirectX: Version 9.0c
• 8800 GT

Recommended System Requirements

• OS: Windows XP, Vista or Windows 7
• CPU: Core 2 Quad 3 GHz
• RAM: 3 GB
• HDD: 15 GB free disk space
• Graphics: 512 MB Graphics Memory
• Sound Card: DirectX 9 Compatible
• DirectX: Version 9.0c
• Geforce GTX 460/Radeon 5850

A Note to those who want to run the game on min settings: 

Please note that, if you are thinking of buying this game when you can only run it on minimum settings, you should think twice. Publishers and Developers would like you to think that you can run the game on the lowest settings possible. To a certain extent, this is true. A PC with the minimum specs, (seen above) can probably run Skyrim, but that game would be running at very low resolution, and would probably have frame rate issues. I personally suggest that if you don't have a PC that can run the game on the recommended settings, than you should probably just stick to the console version.