Anonymous access in SharePoint can be configured on the lists level. This means that anonymous access can be setup to individual lists rather than an entire SharePoint site. It can be also turned on for an entire web site.
The anonymous access is enabled from the web application level first. ISA server (if available) will be also configured.
After a web application has been setup for anonymous access, individual web sites can be configured to enable anonymous access on them. By default, sites have their anonymous access turned off, and must be enabled by a site admin before non-authenticated users can access it. As mentioned earlier, this can also be set on individual lists and will be accessible by a direct link to the list.
MySite and Application pages
Unfortunately, with MOSS 2007, MySites cannot be accessible by anonymous users, and that’s because of the way that has been setup. To make them accessible to the outside users, some workarounds are needed. However, sub sites within MySite can be made accessible to outside users, but not the root MySite.
The Application pages (pages in the _Layouts folder) are also not accessible to the outside users. This includes the search default page. It is possible to solve these problems with some workarounds that involves custom developments.