I have read articles about editing core.js and other complicated ways.. I found an easy way and the best part is its one line of code !
.ms-MenuUIULItem[text='Add to My Links']{display:none !important;}
Replace ‘Add to My Links’ with your choice of menu item to hide.
Here is the source and this is how I figured it out
<li class="ms-MenuUIULItem" type="option" text="Add to My Links" onmenuclick="Portal_Tasks('PinToMyPage')" iconalttext="" sequence="1000" id="mp14_0_10"><div class="ms-MenuUIULItem" type="option" text="Add to My Links" onmenuclick="Portal_Tasks('PinToMyPage')" iconalttext="" sequence="1000"><a class="ms-MenuUIULLink" id="mp14_0_10_Anchor" href="javascript:;" onclick="return false;"><span class="ms-MenuUIIcon" style="white-space: nowrap; "><img class="ms-MenuUIULImg" width="16" height="16" id="mp14_0_10_ICON" src="/_layouts/images/blank.gif" alt="" title=""></span><span class="ms-MenuUILabel" style="white-space: nowrap; " id="ID_AddToMyLinks"><span style="white-space: nowrap;">Add to My Links</span><span></span></span><span style="float: left; width: auto; white-space: nowrap; display: none; " class="ms-MenuUIAccessKey"></span><span class="ms-MenuUISubmenuArrow" style="white-space: nowrap; display: none; "></span></a></div></li>