Assange could face extradition to the US, most probably under the 1917 Espionage Act. Whether he'd be likely to be convicted under this act, is a matter for some debate, but according to this article, recent precedents suggest that he would be found guilty, as would the editors of the New York Times, anyone mirroring copies of WikiLeaks, and perhaps anyone running a web proxy which inadvertently cached the data. (This is in an open court, mind you; in a closed military tribunal, all bets are off.)
Meanwhile, the Russian government has called for Assange to be given the Nobel Peace Prize; somewhat of a change from its usual policy regarding troublesome journalists, it must be said. Still, if I were him, I'd probably run a Geiger counter over the medal first, just to be safe.