How do I know which version of Javascript I'm using?

Click on this link to see which version your BROWSER is using: http://jsfiddle.net/Ac6CT/

You should be able filter by using script tags to each JS version.

<script type="text/javascript">
    var jsver = 1.0;
</script>
<script language="Javascript1.1">
  jsver = 1.1;
</script>
<script language="Javascript1.2">
    jsver = 1.2;
</script>
<script language="Javascript1.3">
  jsver = 1.3;
</script>
<script language="Javascript1.4">
  jsver = 1.4;
</script>
<script language="Javascript1.5">
  jsver = 1.5;
</script>
<script language="Javascript1.6">
  jsver = 1.6;
</script>
<script language="Javascript1.7">
  jsver = 1.7;
</script>
<script language="Javascript1.8">
  jsver = 1.8;
</script>
<script language="Javascript1.9">
  jsver = 1.9;
</script>

<script type="text/javascript">
    alert(jsver);
</script>

　　

My Chrome reports 1.7

Blatantly stolen from: http://javascript.about.com/library/bljver.htm

<script>
function (JSVer());
  // STEP ONE: Convert all characters to lowercase to simplify testing
  var agt=navigator.userAgent.toLowerCase();

  // SETP TWO: Determine Browser Version
  // Note: On IE5, these return 4, so use is_ie5up to detect IE5.
  var is_major = parseInt(navigator.appVersion);
  var is_minor = parseFloat(navigator.appVersion);

  // Note: Opera and WebTV spoof Navigator.  We do strict client detection.
  // If you want to allow spoofing, take out the tests for opera and webtv.
  var is_nav  = ((agt.indexOf('mozilla')!=-1) && (agt.indexOf('spoofer')==-1)
    && (agt.indexOf('compatible') == -1) && (agt.indexOf('opera')==-1)
    && (agt.indexOf('webtv')==-1) && (agt.indexOf('hotjava')==-1));
  var is_nav2 = (is_nav && (is_major == 2));
  var is_nav3 = (is_nav && (is_major == 3));
  var is_nav4 = (is_nav && (is_major == 4));
  var is_nav4up = (is_nav && (is_major >= 4));
  var is_navonly = (is_nav && ((agt.indexOf(";nav") != -1) ||
    (agt.indexOf("; nav") != -1)) );
  var is_nav6 = (is_nav && (is_major == 5));
  var is_nav6up = (is_nav && (is_major >= 5));
  var is_gecko = (agt.indexOf('gecko') != -1);

  var is_ie     = ((agt.indexOf("msie") != -1) && (agt.indexOf("opera") == -1));
  var is_ie3    = (is_ie && (is_major < 4));
  var is_ie4    = (is_ie && (is_major == 4) && (agt.indexOf("msie 4")!=-1) );
  var is_ie4up  = (is_ie && (is_major >= 4));
  var is_ie5    = (is_ie && (is_major == 4) && (agt.indexOf("msie 5.0")!=-1) );
  var is_ie5_5  = (is_ie && (is_major == 4) && (agt.indexOf("msie 5.5") !=-1));
  var is_ie5up  = (is_ie && !is_ie3 && !is_ie4);
  var is_ie5_5up =(is_ie && !is_ie3 && !is_ie4 && !is_ie5);
  var is_ie6    = (is_ie && (is_major == 4) && (agt.indexOf("msie 6.")!=-1) );
  var is_ie6up  = (is_ie && !is_ie3 && !is_ie4 && !is_ie5 && !is_ie5_5);

  // KNOWN BUG: On AOL4, returns false if IE3 is embedded browser
  // or if this is the first browser window opened.  Thus the
  // variables is_aol, is_aol3, and is_aol4 aren't 100% reliable.
  var is_aol   = (agt.indexOf("aol") != -1);
  var is_aol3  = (is_aol && is_ie3);
  var is_aol4  = (is_aol && is_ie4);
  var is_aol5  = (agt.indexOf("aol 5") != -1);
  var is_aol6  = (agt.indexOf("aol 6") != -1);

  var is_opera = (agt.indexOf("opera") != -1);
  var is_opera2 = (agt.indexOf("opera 2") != -1 || agt.indexOf("opera/2") != -1);
  var is_opera3 = (agt.indexOf("opera 3") != -1 || agt.indexOf("opera/3") != -1);
  var is_opera4 = (agt.indexOf("opera 4") != -1 || agt.indexOf("opera/4") != -1);
  var is_opera5 = (agt.indexOf("opera 5") != -1 || agt.indexOf("opera/5") != -1);
  var is_opera5up = (is_opera && !is_opera2 && !is_opera3 && !is_opera4);

  var is_webtv = (agt.indexOf("webtv") != -1); 
  var is_TVNavigator = ((agt.indexOf("navio") != -1) || (agt.indexOf("navio_aoltv") != -1)); 
  var is_AOLTV = is_TVNavigator;

  var is_hotjava = (agt.indexOf("hotjava") != -1);
  var is_hotjava3 = (is_hotjava && (is_major == 3));
  var is_hotjava3up = (is_hotjava && (is_major >= 3));

  // STEP THREE: Associate Javascript Version with Browser
  var is_js;
  if (is_nav2 || is_ie3) is_js = 1.0;
  else if (is_nav3) is_js = 1.1;
  else if (is_opera5up) is_js = 1.3;
  else if (is_opera) is_js = 1.1;
  else if ((is_nav4 && (is_minor <= 4.05)) || is_ie4) is_js = 1.2;
  else if ((is_nav4 && (is_minor > 4.05)) || is_ie5) is_js = 1.3;
  else if (is_hotjava3up) is_js = 1.4;
  else if (is_nav6 || is_gecko) is_js = 1.5;
  // NOTE: In the future, update this code when newer versions of JS
  // are released. For now, we try to provide some upward compatibility
  // so that future versions of Nav and IE will show they are at
  // *least* JS 1.x capable. Always check for JS version compatibility
  // with > or >=.
  else if (is_nav6up) is_js = 1.5;
  // NOTE: ie5up on mac is 1.4
  else if (is_ie5up) is_js = 1.3
  // HACK: no idea for other browsers; always check for JS version with > or >=
  else is_js = 0.0;
  return (is_js) ; 
</script>