In addition to Tim Downs answer, i made a solution that work even in oldIE:
var selectText = function() {
  var range, selection;
  if (document.body.createTextRange) {
    range = document.body.createTextRange();
    range.moveToElementText(this);
    range.select();
  } else if (window.getSelection) {
    selection = window.getSelection();
    range = document.createRange();
    range.selectNodeContents(this);
    selection.removeAllRanges();
    selection.addRange(range);
  }
};
document.getElementById('foo').ondblclick = selectText;
Tested in IE 8+, Firefox 3+, Opera 9+, & Chrome 2+. Even I've set it up into a jQuery plugin:
jQuery.fn.selectText = function() {
  var range, selection;
  return this.each(function() {
    if (document.body.createTextRange) {
      range = document.body.createTextRange();
      range.moveToElementText(this);
      range.select();
    } else if (window.getSelection) {
      selection = window.getSelection();
      range = document.createRange();
      range.selectNodeContents(this);
      selection.removeAllRanges();
      selection.addRange(range);
    }
  });
};
$('#foo').on('dblclick', function() {
  $(this).selectText();
});
...and who's intereseted in, here's the same for all coffee-junkies:
jQuery.fn.selectText = ->
  @each ->
    if document.body.createTextRange
      range = document.body.createTextRange()
      range.moveToElementText @
      range.select()
    else if window.getSelection
      selection = window.getSelection()
      range = document.createRange()
      range.selectNodeContents @
      selection.removeAllRanges()
      selection.addRange range
    return
Update:
If you want to select the entire page or contents of an editable region (flagged with contentEditable), you can do it much simpler by switching to designMode and using document.execCommand:
There's a good starting point at MDN and a littledocumentation.
var selectText = function () {
  document.execCommand('selectAll', false, null);
};
(works well in IE6+, Opera 9+, Firefoy 3+, Chrome 2+) http://caniuse.com/#search=execCommand