What is the best way to add options to a select from a JavaScript object with jQuery?

The same as other answers, in a jQuery fashion:

$.each(selectValues, function(key, value) {   
     $('#mySelect')
         .append($("<option></option>")
                    .attr("value", key)
                    .text(value)); 
});

var output = [];

$.each(selectValues, function(key, value)
{
  output.push('<option value="'+ key +'">'+ value +'</option>');
});

$('#mySelect').html(output.join(''));

In this way you "touch the DOM" only one time.

I'm not sure if the latest line can be converted into $('#mySelect').html(output.join('')) because I don't know jQuery internals (maybe it does some parsing in the html() method)

This is slightly faster and cleaner.

var selectValues = {
  "1": "test 1",
  "2": "test 2"
};
var $mySelect = $('#mySelect');
//
$.each(selectValues, function(key, value) {
  var $option = $("<option/>", {
    value: key,
    text: value
  });
  $mySelect.append($option);
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<select id="mySelect"></select>