This is applicable for SharePoint 2013.
  1. Go to My Learning site -> Site Settings -> Master Pages (under Web Design Galleries)
  2. Download the default master page - seattle.master.
  3. Add the following style in the header of master page:
    <style type="text/css"> #titleAreaBox #SearchBox{ display: none !important; } </style>
  4. If you use custom master page repeat the actions for your master page.
  5. Repeat the actions for all your sites.
The default master page (seattleExample.master) with this enhancement is attached.