In the olden days (like, a couple of years ago) classified documents would get leaked to newspapers. The newspapers would take a look at them and publish them in excerpt alongside an editorial talking about how they thought long and hard about whether it was in the public interest to publish this particular document and blah blah blah. As I understand it, based on my reading of the law, they were technically committing a crime by doing so, but the authorities never bothered to pursue prosecution against the media outlets and just prosecuted the original leaker. Why not? I don't know, maybe because responsible publication of leaks is acknowledged to be a good thing, or maybe because it's not worth going to war with anyone who buys ink by the gallon.

Wikileaks, on the other hand, will publish huge swathes of documents in a much less restrained manner than the New York Times would. It's concievable that they can be charged.

As far as I know, the law states that it's illegal to pass along classified documents, and it doesn't restrict the applicability of this law to the people who were supposed to have the documents in the first place.

Note that this does not apply to Bradley Manning or others who may be sources and who may have committed crimes in passing classified information to uncleared people. But as much as our political elites might wish it; embarrassing the government is not a crime.