To hide the "About me" link in a SharePoint 2013 environment, place the given below css statements in the style sheet library.
<style type="text/css">
.ms-core-menu-list li[text='About Me'] { display: none;}
</style>
* .ms-core-menu-list is the css class name pertaining to the About Me display link.
By setting display: none, the about me link gets invisible!!