Details on SCOTUSBlog (where else), as they become available. Justice Kennedy wrote the majority opinion. The opinions are here.

UPDATE: The Chief Justice and Justice Scalia wrote dissenting opinions (each joined by the usual suspects). Justice Souter wrote a concurrence joined by Ginsburg and Breyer.

FURTHER UPDATE: Lyle Denniston is giving insta-analysis of the opinions here. While it was generally anticipated that the government would lose the case, he calls the decision a "stunning blow to the Bush Administration in its war-on-terrorism policies."

LAST UPDATE: As I (super-quickly) skim Justice Kennedy's opinion for the Court, it appears to hold that Guantanamo detainees have habeas rights, that these rights can only be denied through a valid suspension of habeas rights (under the Suspension Clause of the Constitution), that the procedures created by the Detainee Treatment Act were not an adequate substitute for habeas, and therefore Section 7 of the Military Commission Act is an unconstitutional suspension of the detainees' habeas rights. I'm sure I (and others) will have more to say about this case in subsequent posts.