The background: Dick Heller tried to register a handgun with the District of Columbia, which denied him. DC has banned the registration and thus the possession of all privately owned handguns — no exceptions.
Heller won on the lower level, where the DC Circuit Court ruled 2-1 that there is an individual right to keep and bear arms. In so doing it struck down the DC law.
So that's the background. At the oral argument, predictably, the court seemed to split along ideological lines. Chief Justice Roberts and Justices Alito, Scalia, and likely Thomas are clearly in favor of an individual right to keep and bear arms, while Justices Ginsburg, Souter, Stevens, and likely Breyer favor the other way. This leaves Justice Kennedy in his usual spot: the deciding vote.
While the discussion at oral argument is not a definitive sign of the way a justice is leaning, advocates for the individual right to keep and bear arms have to be heartened by what they heard from Justice Kennedy. Justice Kennedy hints that some past precedent limiting gun ownership "may be deficient."
So what's the conclusion? Perhaps we are going towards "an individual right, but with reasonable regulation." What the reasonable regulation will be is, of course, the primary question. We have to wait for the opinion for that.