Existing Web Application is not listed on New Shared Services Provider page

In order for your Web Application to be visible in the "Web applications" dropdown list on the "New Shared Services Provider" page:

If your installation is "Application" or "Complete" as Setup names it, user identity for the application pool under which the web application is running has to be different from NetworkService.

If you are running a "Single Server" or how setup names it "Stand-alone" installation then application pool user is not taken into account.

TIP: When using stsadm.exe -o extendvs make sure that -apidtype paremeter is set to ConfigurableID and make sure that there is no typo in it, because stsadm will not show any error message. It will set NetworkService user as an application pool user (causing it not to be shown in the dropdown).