Windows Vista can run dx10. It can run dx11 if you install the Platform Update. It depends on your graphics card though. You'll also need fully updated drivers.
To check what version of direct-x you have:
Type "dxdiag" into run, run it, and the last line on the first page will tell you what version of direct-x you have. You can also see what graphics chip you have if you want to look up compatibility/drivers.