Resident Evil 6 lists September 18 for the release of the game's demo on PlayStation Network and for Xbox Live gold members. The demo will be generally available through Xbox Live on September 25.
The Resident Evil 6 demo will be different from that provided to Dragon's Dogma purchasers on Xbox 360. We've contacted Capcom to confirm dates for North America, and we'll update when we hear back.
Update: Capcom has confirmed North American dates are same as those above. Added press release with further details on new demo.