Mozilla recently published a demo of standards-based video chat in an experimental build of Firefox. The functionality is built with the Web Real Time Communication (WebRTC) standard, which aims to support streaming audio and video communication on the Web without relying on plugins.
The WebRTC standard is currently in the draft stage, but it has been endorsed by most of the major browser vendors. Some initial components are already available in several browsers. The underlying technology comes from Global IP Solutions, which Google acquired in 2010. Google opened the source code of the original implementation under a BSD license in order to facilitate its standardization.
The WebRTC support is currently being developed in a Firefox branch. According to a comment from Anant Narayanan of Mozilla Labs, the developers hope to get the feature rolled into the mainline and make it available in nightly builds within the next few months. Google has already rolled out some early WebRTC features, such as the camera access APIs, in the Chrome developer channel. Google added a nice permission dialog last month that will display when a Web application requests access to a camera.
It's worth noting that the WebRTC standard is under heavy development and is still undergoing major revisions. It is being drafted through a WebRTC W3C working group, which announced some major API changes last month. When the dust settles and the standard is mature, it's likely to see widespread adoption, eliminating the need for plugins to enable video chat.