You can delete any dashboard you created and, unless you are logged in as a ReadOnly user, any shared dashboard that is available to you. The only dashboard that cannot be deleted is the Home Page.
When you delete a shared dashboard, a dialog box warns that the dashboard is sharedn. Be careful when deleting a shared dashboard because other console users might want to continue using it. If another user is using a dashboard when you delete it, the dashboard remains displayed until that user navigates away from it, at which point it becomes unavailable.