HTML5 video faces a number of challenges before it can overtake Flash on the desktop, but it has already become a standard on iOS and Android. As LongTail notes, IE 6/7/8 will never support HTML5, but Google Chrome, Mozilla Firefox and the latest version of Internet Explorer all grew their share of the market since January, while non-supportive browsers continue to decline.
One challenge with HTML5 video is its fragmented support for audio/video formats. If nobody agrees on a standard, nothing will ever work across the board. At the moment, Firefox, Chrome and Opera support the WebM format, while IE, Safari, Chrome, iOS and Android support the MP4 format. The good news is that Firefox recently announced that it will soon support MP4.