Is it possible to use Google Sites as a Wiki where everyone can edit without first asking for the owner to allow them?
Actually, I found the answer myself. One can use it as a Public Wiki by using this trick.
Create a Google Group so anyone can join: http://groups.google.com/groups/create?lnk=gcphp
Invite the Group to your Site as a collaborator using its email address, e.g. MyGroup@googlegroups.com
Put a link to your Google Group on your Site, preferably on your homepage or sidebar, and a notice inviting those who are interested to join.
Now anyone who subscribes to your Group automatically gets to edit your Site too.