Those are breadcrumbs. You can completely remove them from all pages by adding the following line into your own layout.xml file.
<remove name="breadcrumbs.container"/>
You can define your own layout.xml file for your module by adding something like the following into your magento modules config.xml
<frontend>
<layout>
<updates>
<namespace_module modules="Namespace_Module">
<file>namespace_module.xml</file>
</namespace_module>
</updates>
</layout>
</frontend>
Then the layout.xml
file would look something like
<?xml version="1.0" encoding="UTF-8"?>
<layout>
<default>
<remove name="breadcrumbs.container"/>
</default>
</layout>