YouTube's 3D mode has been extended to add a new mode of display, with the addition of support for NVIDIA's 3D vision - so far only in Firefox 4. The reason for the restriction to one browser is that the videos are using the WebM format - a video codec supported, among others, by Google and Mozilla, explaining their teaming up
Viewers with Firefox 4 and a 3D vision-capable NVIDIA graphics card will be able to select HTML 5 Stereo Mode on 3D videos on YouTube. Currently, doing so requires diving into a separate menu and back to the video of chosen, but as NVIDIA is offering a simple website which lets you check if your browser GPU can support stereoscopic YouTube it's likely auto-detection will be added once YouTube is happy there are no issues with this new 3D mode.
Without compatible hardware and software the old 3D options offered by YouTube - including interleaved, side-by-side and two-colour glasses modes - will still be available. The quality of these methods of displaying of 3D is a marked step down from stereoscopic, however.
Although the feature is currently only available in Firefox 4, Mozilla is keen for other browsers to follow it in supporting the new 3D mode. Chrome would be the most likely next candidate, as it also already supports the WebM format - Internet Explorer support is almost certainly off the cards, though.