The Supreme Court held that the Geneva Conventions do apply to the "war on terror", specifically mentioning Article 3 of the Geneva Conventions. For the attention-reduced, here's the short form.
In the case of armed conflict not of an international character occurring in the territory of one of the High Contracting Parties, each party to the conflict shall be bound to apply, as a minimum, the following provisions:
1. Persons taking no active part in the hostilities, including members of armed forces who have laid down their arms and those placed hors de combat by sickness, wounds, detention, or any other cause, shall in all circumstances be treated humanely, without any adverse distinction founded on race, colour, religion or faith, sex, birth or wealth, or any other similar criteria.
To this end the following acts are and shall remain prohibited at any time and in any place whatsoever with respect to the above-mentioned persons:
(a) Violence to life and person, in particular murder of all kinds, mutilation, cruel treatment and torture;
(b) Taking of hostages;
(c) Outrages upon personal dignity, in particular, humiliating and degrading treatment;
(d) The passing of sentences and the carrying out of executions without previous judgment pronounced by a regularly constituted court affording all the judicial guarantees which are recognized as indispensable by civilized peoples.
2. The wounded and sick shall be collected and cared for.
An impartial humanitarian body, such as the International Committee of the Red Cross, may offer its services to the Parties to the conflict.
The Parties to the conflict should further endeavour to bring into force, by means of special agreements, all or part of the other provisions of the present Convention.
The application of the preceding provisions shall not affect the legal status of the Parties to the conflict.
Now, doesn't that mean that absent compliance with the Conventions, President Bush and his cronies could be tried for war crimes? Attorney General Alberto Gonzalez is famous for referring to the Geneva Conventions as "quaint". Clearly, the White House still believes that, because they immediately started to look for Congressional work-arounds to avoid the consequences of the Court's decision.
The Justices also said that this decision says nothing about the future of Guantanamo itself. OK, I see that. But (and I'm no lawyer) the decision ruled that the Bush administration's decision to try the detainees at Guantanamo in military war trials is illegal. Presumably then, they must be tried either in federal court, in military courts martial, or the detainees would have to be repatriated and tried in their home countries. I'm actually wondering if this decision doesn't give the White House a graceful out re: closing the prison that has become a political liability. They could take the self-serving position that they tried to protect the people from the evil represented by these (untried and uncharged) people held in detention, but the Supreme Court tied their hands. They save face and the prison is closed.
And then some enterprising lawyers could set about the business of trying the entire administration for crimes against humanity.