Implementations in Web browsers
List of known implementations of HTML 5 in web browsers (list is incomplete, feel free to extend it)
For summary see Comparison of layout engines (WHATWG) in Wikipedia.
Web Applications 1.0
getElementsByClassName implemented in Firefox 3
Client-side session and persistent storage implemented in Firefox 2
Custom content handlers partly implemented in Firefox 2
ping attribute implemented in Firefox 3
Cross-document messaging implemented in Opera 9
Audio interface implemented in Opera 9
Server-sent DOM events implemented in Opera 9
Web Forms 2.0
In Opera 9 are natively implemented all extensions to the input element.
date input element with input-type-date works in Firefox, IE6/7, Safari
Project  emulate in IE6/7 validation, date and time types, range, repetition, calculated fields, datalist, autofocus.
Web Controls 1.0