Most major websites nowadays have mobile versions. Some examples include Google, Yahoo, and Reddit. Up until recently, most mobile websites were built using the wap/wml (wireless application protocol) format. The WAP format can be thought of as a compressed version of HTML. If you view the source for the CNN site, you can see its header DOCTYPE set as so:

< ?xml version="1.0" ?>
< !DOCTYPE html PUBLIC "-//WAPFORUM//DTD XHTML Mobile 1.0//EN" "http://www.wapforum.org/DTD/xhtml-mobile10.dtd">

Most sites have a special URL dedicated to mobile devices (e.g. m.site.com, mobile.site.com). If the user decides to browse to site.com instead of m.site.com, some redirect code can be added to the main site to determine the user agent (browser), and redirect accordingly. Dev.mobi offers a PHP script to determine whether a browser comes from a mobile device, using variables such as php's $_SERVER['HTTP_USER_AGENT'].

Full HTML support is also being more widespread as more advanced mobile devices are hitting the market. Even as mobile browsers are becoming more indistinguishable from their full-size counterparts, and as cellular networks are getting faster, there are still several considerations to take seriously:

1. Download size is still an important issue.
There are people out there paying $2/MB for data usage. It's fine to show a small, compressed logo image, but if you stick on a useless 75KB stock image, you're going to inadvertently piss some people off. With that being said, code optimization is also extremely important. Many IA rules apply to both desktop and mobile websites (latest or featured content up top), but this matters more on mobile devices since it's often harder to scroll around and what not.

2. Design must be flexible
Mobile devices come in a myriad of different forms and screen sizes. Some browsers support javascript and/or Flash (lite), but not all. Fixed-width mobile sites are all but unheard of. If your site is complex in design and you'd prefer to keep it intact, then it may save headaches in the long-term by not supporting mobile versions and hoping that more iPhone-like devices (with full HTML support) roll their way onto shelves. To try out mobile versions without a lot of time invested, there are services such as MoFuse that'll automatically build a mobile website version for you.