A split decision. Three out of four provisions were judged to be unconstitutional violations of federalism (state interference with national powers), but the major component of it - which allowed local police to inquire about the citizenship status of people they stop or arrest - was found constitutional, unanimously.
From the NYT:
The court unanimously sustained the law’s centerpiece, the one critics have called its “show me your papers” provision, though they left the door open to further challenges. The provision requires state law enforcement officials to determine the immigration status of anyone they stop or arrest if they have reason to suspect that the individual might be in the country illegally.
The justices parted ways on three other provisions, with the majority rejecting measures that would have subjected illegal immigrants to criminal penalties for activities like seeking work.
The ruling is likely to set the ground rules for the immigration debate, with supporters of the Arizona law pushing for “show me your papers” provisions in more states and opponents trying to overturn criminal sanctions for illegal immigrants.
Writing for the majority, Justice Anthony M. Kennedy said, “Arizona may have understandable frustrations with the problems caused by illegal immigration while that process continues, but the state may not pursue policies that undermine federal law.”
An interactive look at the decision.
Scotusblog has several posts on the subject.