In recent months Internationalized Domain Names -- url's and email addresses written in scripts other than Latin -- have been set up for testing by ICANN. You can see whether your browser is equipped to handle the IDNA protocol which these use by clicking on links at the bottom of this page. You can similarly test your email client here.
Note the difference in what appears in the browser address bar when you point Safari at the topmost (Arabic) site and the (9th down) Russian site. The former will be in the native script, while the latter will be in an ASCII translation called Punycode. This is done because Russian script and Roman script can be confusable and create security problems. Which scripts generate Punycode is determined by a "whitelist" in the Safari app. Info on this and other aspects of Safari support for IDNA can be found here.
IDNA is currently limited to the range of scripts included in Unicode 3.2 in 2002. Since then nearly 30 more have been added, and the IETF is working on an update that will accommodate Unicode 5.1 and any future version