Google Chrome and Mozilla Firefox are pushing HTML5. An open and (relatively) powerful standard is in their interest.
Opera is trying, but its small market share makes it irrelevant (sorry to say that) - it is a good software, but they do not have a killer feature that would lead more people to them. Good compatibility is not enough, especially when sites are optimized for other browsers.
Internet Explorer has been successfully (intentionally) slowing down the adoption of new web technologies in the last decade. Powerful web apps are Microsoft's nightmare. Once ordinary users only need a capable internet browser, Windows loses a lot of ground. (Why install Windows on your mom's computer when she only needs it for reading email, video-conferencing, watching news, TV shows and movies, listening to music and playing games like solitaire? And all that can be done in a free HTML5 browser running on a free Linux.)
Microsoft continues to sabotage the progress with IE9 by claiming HTML5 compatibility and calling it a modern browser. They only implemented a tiny bit of HTML5 and are discrediting the HTML5 buzzword. That behavior is completely understandable, it has brought them a lot of money. They were the leader in IE4 times, but left that position to others. Maybe they make a comeback - they had 10 years to address the situation and I kind of do not want to believe that their whole strategy was to delay the adoption of web technologies. We'll see...