I know the target audience for most of my sites so I don't worry too much about different screen resolutions. I doubt that many clients would want to pay for different versions of a site, but I just read about a tool that makes it relatively easy to develop a site that will work with different screen resolutions. The tool, called Less Framework 3, creates a framework that recognizes the visitor's screen resolution and sizes the web page accordingly. The framework is based on four different layouts to accommodate the majority of screen resolutions:
3-column–For all iPhones, iPod Touches, and other 320 px mobile devices
5-column–For 480 px mobiles, narrow browsers, and landscape iPhones
8-column–For tablets at 768 px, netbooks, and old browsers
13-column–For laptops, desktops, and HDTVs at 1280 px and beyond
You can read more about Less Framework 3 and see it in action at http://lessframework.com/.