I presume the US$, but why does that matter?
Unless you're thinking something along the lines of Saudis accepting Renmimbi and Rupies as payment, without converting them to USD first, in which case international demand for the US buck goes down, such that the value of the USD drops. (having the USD being the international currency is part of what props up its value).
In that case, from an American point of view, Saudi oil becomes more expensive, providing even more incentive for the US to improve the technology to exploit its own tougher-to-reach resources.
It also would make the relative cost of Chinese products go up, which would bring back incentive for Americans to build things at home, thus re-creating manufacturing jobs.
Reduction of the value of the USD would also, in relative terms, reduce the value of the American debt to China (unless those debts are measured in Renmimbi, which I doubt).
Overall I see no problem, and maybe even a long-term benefit to the American people, if the USD were to no longer be the world standard.
Presuming the demand is constant, but demand from India and China is going up, so that should maintain the level of "demand" that OPEC is accustomed to... no?