Regardless of the underlying operating system, HTML5 promises the ability to run applications platform-independant. Already being confirmed to be supported by Microsoft, Google, and Mozilla it is more than likely that all major browsers are going to feature an updated interpreter for the new version of the web programming language.
HTML 5 is currently in the developing stage and more than likely to remain in it for a few more years. Despite that, "its focus on running applications within the browser is an important driver of interest in cloud computing, where applications live somewhere off on the Internet and are delivered by the browser.
The focus of future browsers will shift from "going places" to "doing things." This will be a boon to free operating systems, which will increasingly be able to hide themselves under the browser user interface. While Windows and Mac OSX won't go away overnight, the pressure on them will be to innovate beyond the browser, perhaps through a common set of extensions for HTML5 applications to use."