<p>In the past, some of my projects have required me to create a movie version of a fullscreen Flash application. The easiest way to do this has been to get a screen capture. However, capturing anything over 1024x768 has resulted in choppy video, which is unacceptable. I understand that there are hardware based solutions for capturing fullscreen video, but I have not been able to find out what these are. My output needs to be scalable up to 1920x1080 and result in an uncompressed AVI file with no choppy-ness.</p>

With a bit of luck your graphic adapter already has a analog video output. You could hook up a dvd recorder and just digitze the video signal on a stand alone hardware box.
That won't give you 1920x1080 though.
If you really need to get captures higher than dvd resolution you need professional (and
incredible
expensive) video capture equipment.
edit:
Btw - if you want to capture 1920x1080 in true color at 30 frames per second uncompressed you have to somehow store around
237 megabytes per second
. Just to give you an idea how much data you have to deal with...