I was managing a site where all the users were having read access the main site. So they can not create any new site under this site. I had a requirement where a set of users should have only read permission on the home page but they should be allowed to create new sub sites if required.
SharePoint security model is very flexible and if we understand the permissions and permission level properly these kind of scenarios can be solved easily. So for solving this I have created a new permission level copying the the Read Permission level and then adding an additional permission called 'Create Subsites'.
This permission level was assigned to a new SharePoint group and all the user who need to have access to create sub sites has been added into this group. Now when the users from this group access to this SharePoint site they can see the Site Action button. And once they go inside this they can see only one link which is "Sites and Workspaces"
Also users can see the Create Menu option. They can see three links which are shown in the screen shot. The first two links does not work and says that users does not have access. But the third link works and the users are able to create the sub sites into the site in which they are only reader.