Find the relevant code in the following template files and either display:none or remove the relevant lines of code:

product/compare/list.phtml
product/list.phtml
product/new.phtml
product/view/type/default.phtml
product/view/type/grouped.phtml
product/widget/new/column/new_default_list.phtml
product/widget/new/content/new_grid.phtml
product/widget/new/content/new_list.phtml