You gave me an excuse to use my Kill-A-Watt replacement, the Belkin Conserve energy monitor.
Here's my results with some quick tests:
On but doing nothing: 1.7W
Streaming a movie (SD): 2.3W (iTunes)
Streaming a movie (HD): 2.3W (iTunes)
Streaming music: 1.7W (iTunes)
YouTube: 1.9W
Netflix: 1.8-2.1W
Sleep: 0.9W
Very nice overall!
The old Apple TV used to constantly draw around 22W if I remember correctly (I can check if anyone cares), so we're talking about a VAST improvement!