When I leave Law School to go home in April, I will be running it on my ATI Radeon 9600, which is actually the worst ATI card supported by the game. It should be alright on lower settings, at least.
For now, I am stuck with my laptop, which only has an Intel 945G.
It runs SHIII, despite the fact that it is not supported by that game, but it will not run SHIV at all (although I can load up the game, the actual gameplay itself won't work - just the menu screens and cinematics).