According to this new study, 5%. The study was done by comparing the one large group of Americans who can't sue their health care providers – active duty military personnel – with those in comparable insurance plans who can sue. They find that doctors who can be sued order more tests and so on, and that this adds up to 5% more spending.
It's nice to have that information about the direct effect of lawsuits, but I don't think that's the whole story. Most doctors practice according to norms, that is, they do what everyone else is doing. That applies to military doctors as well as private ones. Military doctors could be prescribing things that add nothing to our health because these have become the norms of practice, and those norms could have been shaped by fear of lawsuits. So the real amount of the effect could be greater. Or less, I guess, this being just one study.
I think a bigger factor in driving up costs is the pressure from patients; if you want an expensive procedure or medicine that your doctor won't prescribe you can always just find another doctor who will, and doctors don't like losing customers any more than any other businessmen.
To put it differently, I think the biggest factor making American health care more expensive is that neither doctors nor patients have much incentive to seek lower costs. Most of the costs are born by someone else, either insurance companies or the government, so the question of cost enters into these decisions only when insurance won't pay.