Here's a code fragment to track outgoing links with Google Analytics. As usual, use it at your own risk. I can not give you support for Google products, for obvious reasons.

To use it, you need at least understand where to put it (call it in a try-catch in onLoad) and how to adjust the variable name of your page tracker (I'm not using the default).

function trackLinks(){
  var as=document.getElementsByTagName("a");
  var ig=["mydomain.tld","google-analytics.com"];
  for(var i=0; i<as.length; i++) {
    var ignore=false;
    var oc=as[i].getAttribute("onclick");
    if(oc!=null){
      oc=String(oc);
      if(oc.indexOf('urchinTracker')>=0
      || oc.indexOf('_trackPageview')>=0
      || oc.indexOf('javascript:')>=0)
        continue;
    }
    if(as[i].href.indexOf("mailto:")<0){
      for(var j=0;j<ig.length;j++){
        if (as[i].href.indexOf(ig[j])>=0)
          ignore=true;
      }
    }
    if(!ignore){
      as[i].onclick = function(){
        var o=this.href.replace(/:\/*/,"/");
        pt._trackPageview('/out/'+o)+";"
        + ((oc!=null)?oc+";":"");
      };
    }
  }
}

This code tries to attach an onload handler to any outgoing link, ignoring internal links or links that use JavaScript. If such a link is clicked, it generates a virtual page access with an "/out/" URL that can be analyzed in Google Analytics.

A side benefit (apart from knowing which links are interesting to your visitors) is that you should get more accurate "time on page" statistics for your pages.