What is the most efficient way to sort an Html Select's Options by value, while preserving the currently selected item?

Extract options into a temporary array, sort, then rebuild the list:

var my_options = $("#my_select option");
var selected = $("#my_select").val();

my_options.sort(function(a,b) {
    if (a.text > b.text) return 1;
    if (a.text < b.text) return -1;
    return 0
})

$("#my_select").empty().append( my_options );
$("#my_select").val(selected);

Mozilla's sort documentation (specifically the compareFunction) and Wikipedia's Sorting Algorithm page are relevant.

If you want to make the sort case insensitive, replace text with text.toLowerCase()

The sort function shown above illustrates how to sort. Sorting non-english languages accurately can be complex (see the unicode collation algorithm). Using localeCompare in the sort function is a good solution, eg:

my_options.sort(function(a,b) {
    return a.text.localeCompare(b.text);
});

Modified Tom's answer above slightly so that it actually modifies the contents of the select box to be sorted, rather than just returning the sorted elements.

$('#your_select_box').sort_select_box();

jQuery function:

$.fn.sort_select_box = function(){
    // Get options from select box
    var my_options = $("#" + this.attr('id') + ' option');
    // sort alphabetically
    my_options.sort(function(a,b) {
        if (a.text > b.text) return 1;
        else if (a.text < b.text) return -1;
        else return 0
    })
   //replace with sorted my_options;
   $(this).empty().append( my_options );

   // clearing any selections
   $("#"+this.attr('id')+" option").attr('selected', false);
}

I've just wrapped Mark's idea in a jquery function

$('#your_select_box').sort_select_box();

JQuery function:

$.fn.sort_select_box = function(){
    var my_options = $("#" + this.attr('id') + ' option');
    my_options.sort(function(a,b) {
        if (a.text > b.text) return 1;
        else if (a.text < b.text) return -1;
        else return 0
    })
   return my_options;
}