Fresh install of COD: Anonymous users get "Access denied" on homepage
The permission required is View published content.

It turns out the content access module has a lot of different permissions that can be assigned to roles and this one is not selected by default for anonymous users.

This is a really easy permission to miss. It sits deep within nodes permissions and if you use the search facility for words like view or access you won't get it in the search result. Heck, if you search View published content it isn't returned.