Thumb drives were banned in 2008 after a malware scare, but the ban hasn't been incredibly effective. In 2010, Bradley Manning used thumb drives (as well as CDs) to snag classified information. Certain employees carry thumb drives as part of their job, but they've been given special permission.
Investigators have supposedly discovered exactly what documents Snowden took and where he took them from, though they haven't disclosed if he possesses more documents than the ones he's leaked. Snowden is now the subject of an FBI criminal investigation and the bureau intends to prosecute him.
via The Verge