With ICANN approving the first full Internationalised Domain Names for non-latin scripts such as Arabic, Cyrillic, Chinese, etc do all browsers support these character sets out of the box?
ICANN's blog have lot of info about it.
All major browsers support it (IE, FFox, Chrome, Opera, Safari) according to ICANN.
I tried visiting the greek version of ICANN http://παράδειγμα.δοκιμή in IE8, FFox 3.6, Chrome 4.1, and Opera 10.53
All them shows the page correctly. Chrome and IE8 convert the address to latin characters: http://xn--hxajbheg2az3al.xn--jxalpdlp/%CE%91%CF%81%CF%87%CE%B9%CE%BA%CE%AE_%CF%83%CE%B5%CE%BB%CE%AF%CE%B4%CE%B1
The issue with both browsers is they need the language to be added in their preferences page.
Note they accept the URL out of the box, anyways they can't display it. Also note that α is the greek equivalent to latin a so those browsers "convert" the URL to latin set.
Go to http://blog.icann.org/2010/05/idn-usability/ and try the links to different locales (greek, arab, chinesse, yiddish...)
This post can be interesting too: http://news.cnet.com/8301-1023_3-20004429-93.html