In my testing it works on FireFox 3.6 and above and Chrome 10 and above. Not all effects like page transitions seem to work though.

It looks awful in IE8.

jQuery Mobile doesn't seem to actively ensure that it works on any particular desktop browsers like it ensures that it works on particular mobile browsers. Because of this, you will not have the security of knowing that the next jQuery Mobile release has been rigorously tested on desktop browsers. To ensure it works for the desktop browsers you want it to, you'll have to test it on your own.

That being said, from experience it tends to work well on any up to date desktop browser I've tried it on. This isn't much of a surprise since desktop browsers are so mature and have the added advantage of access to a fast processor and lots of memory. Because there are so few commonly used desktop browsers out there, it shouldn't be too hard to test out your app on all of them every now and then.

• Chrome Desktop 11-13 - Tested on OS X 10.6.7 and Windows 7
• Firefox Desktop 3.6-4.0 - Tested on OS X 10.6.7 and Windows 7
• Internet Explorer 7-9 - Tested on Windows XP, Vista and 7 (minor CSS issues)
• Opera Desktop 10-11 - Tested on OS X 10.6.7 and Windows 7

For the full list check here: http://jquerymobile.com/demos/1.0rc1/docs/about/platforms.html