When you activate anonymous access on a site and you would like your anonymous users to be able to publish an item to a list, then you cannot use the template “Publishing portal”. Why? Don’t know! You must use the template “Team Site” for this to work! I noticed this when I had activated anonymous access but never got rid of the login-prompt! So.. I created a new site and used the template “TeamSite” and enabled anonymous access on it, then voila – an anonymous user was able to post an item to my list without being prompted with the login! Strange….