I'm looking for a reference that summarizes all of the available Javascript APIs that are introduced with HTML 5, for each browser that has implemented any of the new features. Does something like this exist? If nothing else, then at least the VIDEO tag
You can have a look at the last Working Draft of HTML 5, specifically the section about the <video>
element. It contains some samples of Javascript.
But remember that it is of course still a working draft and liable to change. Moreover, as history shows browsers can have different implementations of what the specs say. In the Working Draft there are yellow annotations regarding browser support.
Furthermore, you can read the specifications of ECMAScript 5, to see what browsers may support (but this has nothing to do with HTML5 as such).
Some official stuff is here: http://dev.w3.org/html5/html4-differences/#apis. A site with some sweet demos of the new features is here though: http://html5demos.com/ (You can view source to see the code). The resource that Marcel pointed out is also a good one.