The news is somewhat abuzz with the news that US forces will leave Iraq due to a lack of immunity. On the surface, this seems like a case of hubris that could leave US forces looting and stealing willy nilly! Really, it's a little more subdued.
A couple disclaimers. First, I Am Not A Lawyer (IANAL). Second, my dealing with Status Of Forces Agreements (SOFA) is based on knowledge from me not getting in trouble and snippets from pre-deployment briefs.
Immunity typically does not mean that US forces can break the law, merely that US forces are not subject to local prosecution and justice. If a soldier is arrested they will (depending on the specific SOFA) be taken back by the US embassy and then prosecuted according to US Law with all the rights and privileges thereof. That's not to say that US forces are always bailed out, but they usually are. The biggest end result is that US forces are not exposed to standards of evidence and proof that fall short of US systems or that the soldiers are not punished in cruel and unusual ways.
For more specifics, contact your local Judge Advocate General.