A fan asked about video recording of cool stuff at Blizzcon, and got a reply from Bashiok:
If you’re really interested in this type of streaming the press room at the event will have all of the necessary information on recording restrictions to make sure you’re following the rules.
If you just want to record panels with your handycam to take home and maybe play for your friends or something, I don’t believe there is any restriction.
There’s no recording or pictures allowed in any amount of the live playable demos.
As Bashiok says, Blizzcon bans any recording of the screens. Theoretically this is the case at other events, but we sawfrom PAX and Gamescom last year, where there were fewer staff on hand to kindly ask fans to refrain from recording the screens.