So technically most of what is regularly called 'HTML5' isn't really part of any HTML standard -- i.e., many APIs aren't included in either the W3C or WHATWG HTML specs.
To stay abreast of some of the most useful modern APIs, Rich Clark recently selected what he thinks are the most important, and what seem to far to be, the most popular 'HTML5' APIs. Rich explains:
Alongside those in the specification are a number of related APIs that form part of the standards stack and are often grouped under the "HTML5" umbrella term. In some cases the APIs have been around and implemented for a while, but they've never been documented; something which HTML5 has set out to change.
In this article we're not going to look at code but instead we'll focus on describing the APIs, their purpose and progress. We'll then point you in the right direction to find out more.
Rich's explanations are clear and straightforward. He also links to tons of relevant resources -- specs, W3C community groups, polyfills, hard-core coding deep dives.
Definitely worth checking out for a quick catch-up on the HTML5-as-a-platform APIs, and probably worth bookmarking for future reference.
For a more comprehensive list, with many more APIs (including some of the less sexy, like navigation timing or history), but less discussion and fewer links, try Erik Wilde's HTML5 Landscape Overview. Here's how he describes his list:
Given this focus of HTML5, it is surprisingly hard to find a good place where all the APIs under development are listed. This page is an attempt to collect that information in one place. Since the HTML5 landscape is changing fairly quickly, it is likely that some information on this page is outdaed.
Erik's overview is also worth saving, and keeping updated as technologies change. (Pretty likely to receive strong community support, too, and hence higher likelihood of accuracy, since it enjoys a very high Google pagerank.)