I tested AirPlay with HD and SD videos from the Videos app, and it worked great. I was also able to use AirPlay with the YouTube app. AirPlay didn't work, however, when I tried to play back a movie trailer from Apple's trailers site using the iPad's Safari Web browser. And several other apps I tried, which do support video playback, simply wouldn't work with AirPlay--they would display an AirPlay menu, but my Apple TV only showed up as an audio-capable device. (In other words, I could play back my video's soundtrack on my TV set, but the video would only show up on the iPad.) Presumably developers will be able to update their apps to take better advantage of AirPlay; it sure would be nice to play back live game video from the MLB At Bat app on my TV set when baseball season comes around again.
But before you think that AirPlay opens the door for apps to do crazy stuff, like showing the output of your favorite game app on your HDTV or playing back random video formats from apps such as VLC Media Player, let me explain how AirPlay video streaming works: One device sends a complete, intact video stream to the Apple TV. That video stream is the actual stream of bits of the video file stored on the iOS device (or, in the case of iTunes, on the Mac or PC's hard drive). The device the media files are streaming from isn't processing them in any way--it's just forwarding them on to the Apple TV, which then decodes them and displays them on your TV. As a result, AirPlay only works with video formats that the Apple TV supports.
If you tried to throw an MKV-formatted video you downloaded at your Apple TV, it just wouldn't work. Likewise, the output of a game app would have to be encoded into an Apple TV-compatible format. AirPlay already comes with a two-second buffering delay; throw in the time it would take to encode video and the output of your game would be impossibly out of sync with your iOS device.
One interface quirk of AirPlay on iOS devices that I didn't like is its requirement that you begin to play a video before sending playback to the Apple TV. On a Mac running iTunes, once you select an AirPlay device as your output destination, it uses that device until you tell it to stop or until that device vanishes from the network. It's a much better approach than having to start something playing, then quickly switch to the Apple TV via the AirTunes icon every single time.
Finally, AirPlay is for more than just video: You can also use it to share photos from within the iOS Photos app. In normal browsing mode, your TV mirrors what's on your iPhone or iPad, with just a two-second delay. Flip into slideshow mode, and the contents of your slideshow (music included) will play back on your TV while your iOS device shows a placeholder graphic.