There are a few different ways you can get custom links into the SharePoint 2013 suite bar.  This is the blue bar above the ribbon at the very top of the page.  This method is going to utilize jQuery to inject these links as the page loads and has the added benefit of working in SharePoint Online as well.  It is very simple really, just a few lines.  This will need to go in your master page if you want the links to appear on all of your pages.  It would be possible to just put the contents below into a Content Editor web part if you just wanted the links inserted on an individual page.  You can add as many links as you need, as long as they fit in the bar.  Just repeat lines 9-11 for each new link.

   1: <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.js" type="text/javascript"></script>
   2: <script type="text/javascript">
   3:  
   4:     var $s = jQuery.noConflict();
   5:     $s(document).ready(function() {
   6:         var linkString = "<li class='ms-core-suiteLink'> \
   7:                             <a class='ms-core-suiteLink-a' href='http://www.firsturl.com'>First Link</a> \
   8:                           </li> \
   9:                           <li class='ms-core-suiteLink'> \
  10:                             <a class='ms-core-suiteLink-a' href='http://secondurl.com'>Second Link</a> \
  11:                           </li>";
  12:         $s('.ms-core-suiteLinkList').prepend(linkString);
  13:     });
  14: </script>

 

onprem

The code is a bit different for SharePoint online within Office 365.  The underlying structure is a bit different, so we have to build the links differently and target them to a different div element.  repeat lines 13-19 for each new link that you need to add.  There are so many links already in that space in Office 365, so you may only be able to fit 1 or 2 anyway.

   1: <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.js" type="text/javascript"></script>
   2: <script type="text/javascript">
   3:  
   4:     var $s = jQuery.noConflict();
   5:     $s(document).ready(function() {
   6:         var linkString   = "<div class='o365cs-nav-O365LinksItem'><div> \
   7:                             <a title='First Link' \
   8:                             class='o365button o365cs-nav-navItem o365cs-nav-workloadLink o365cs-spo-topnavLink o365cs-topnavLink' \
   9:                             id='O365_MainLink_ShellMail' role='menuitem' aria-disabled='false' aria-selected='false' \
  10:                             aria-label='First Link' href='http://firsturl.com'><span>First Link</span> \
  11:                             <div class='o365cs-activeLinkIndicator o365cs-nw-b' style='display: none;'></div></a> \
  12:                             </div><div style='display: none;'></div></div>";
  13:             linkString +=  "<div class='o365cs-nav-O365LinksItem'><div> \
  14:                             <a title='Second Link' \
  15:                             class='o365button o365cs-nav-navItem o365cs-nav-workloadLink o365cs-spo-topnavLink o365cs-topnavLink' \
  16:                             id='O365_MainLink_secondLink' role='menuitem' aria-disabled='false' aria-selected='false' \
  17:                             aria-label='Second Link' href='http://secondurl.com'><span>Second Link</span> \
  18:                             <div class='o365cs-activeLinkIndicator o365cs-nw-b' style='display: none;'></div></a> \
  19:                             </div><div style='display: none;'></div></div>";
  20:         $s('.o365cs-nav-O365Links div:first').prepend(linkString);
  21:     });
  22: </script>

 

As you can see, there is more code, but the outcome is essentially the same:

online