The NRA's ILA has a collection of legal documents available, including a link to the transcript ( note: PDF ) published by the Supreme Court.
There's a great quote in the transcript I heard on NPR, but haven't heard anywhere else.
CHIEF JUSTICE ROBERTS: What is -- what is reasonable about a total ban on possession?
MR. DELLINGER: What is reasonable about a total ban on possession is that it's a ban only an the possession of one kind of weapon, of handguns, that's been considered especially -- especially dangerous. The --
CHIEF JUSTICE ROBERTS: So if you have a law that prohibits the possession of books, it's all right if you allow the possession of newspapers?
This is exactly what many supporters of the right to keep and bear arms have wanted; treat the 2nd Amendment in the same way the rest of the Bill of Rights is treated.
Note that this wouldn't mean unrestricted access to firearms in the US. Just as libel isn't protected speech, there would seem to be some restrictions that the Government can place on the right to keep and bear arms which would not violate individual rights.
While the Supreme Court, in oral arguments, did seem to support that the 2nd Amendment is an individual right, there seems some debate on what restrictions are "reasonable":
If it goes without saying that the nation is divided over gun laws, the Supreme Court certainly seemed to mirror that split during arguments today challenging the District of Columbia's handgun ban. Though many justices appeared to lean in favor of an individual right, they diverged over whether such a decision would still allow D.C.'s law to stay in place.
As a reminder, the restrictions in Washington DC boil down to:
- No private ownership of handguns.
- Private rifles and shotguns must be kept either disassembled or with trigger locks, rendering them useless for immediate self defense.
The effectiveness of those restrictions on crime in DC is, to put it mildly, a matter of no small debate.
A decision from the Supreme Court is due in June.
 Ok, ok... non-US readers can be forgiven for missing the intricacies of US politics ;)