jQueryUI: how can I custom-format the Autocomplete plug-in results?

Yes, you can if you monkey-patch autocomplete.

In the autocomplete widget included in v1.8rc3 of jQuery UI, the popup of suggestions is created in the _renderMenu function of the autocomplete widget. This function is defined like this:

_renderMenu: function( ul, items ) {
    var self = this;
    $.each( items, function( index, item ) {
        self._renderItem( ul, item );
    });
},

The _renderItem function is defined like this:

_renderItem: function( ul, item) {
    return $( "<li></li>" )
        .data( "item.autocomplete", item )
        .append( "<a>" + item.label + "</a>" )
        .appendTo( ul );
},

So what you need to do is replace that _renderItem fn with your own creation that produces the desired effect. This technique, redefining an internal function in a library, I have come to learn is called monkey-patching. Here's how I did it:

  function monkeyPatchAutocomplete() {

      // don't really need this, but in case I did, I could store it and chain
      var oldFn = $.ui.autocomplete.prototype._renderItem;

      $.ui.autocomplete.prototype._renderItem = function( ul, item) {
          var re = new RegExp("^" + this.term) ;
          var t = item.label.replace(re,"<span style='font-weight:bold;color:Blue;'>" + 
                  this.term + 
                  "</span>");
          return $( "<li></li>" )
              .data( "item.autocomplete", item )
              .append( "<a>" + t + "</a>" )
              .appendTo( ul );
      };
  }

Now, this is a hack, because

there's a regexp obj created for every item rendered in the list. That regexp obj ought to be re-used for all items.

there's no css class used for the formatting of the completed part. It's an inline style.
This means if you had multiple autocompletes on the same page, they'd all get the same treatment. A css style would solve that.

...but it illustrates the main technique, and it works for your basic requirements.

working example: http://jsbin.com/ezifi/4

To preserve the case of the match strings, as opposed to using the case of the typed characters, use this line:

var t = item.label.replace(re,"<span style='font-weight:bold;color:Blue;'>" + 
          "$&" + 
          "</span>");

In other words, starting from the original code above, you just need to replace this.term with "$&".

EDIT
The above changes every autocomplete widget on the page. If you want to change only one, see this question:
How to patch *just one* instance of Autocomplete on a page?

this also works:

       $.ui.autocomplete.prototype._renderItem = function (ul, item) {
            item.label = item.label.replace(new RegExp("(?![^&;]+;)(?!<[^<>]*)(" + $.ui.autocomplete.escapeRegex(this.term) + ")(?![^<>]*>)(?![^&;]+;)", "gi"), "<strong>$1</strong>");
            return $("<li></li>")
                    .data("item.autocomplete", item)
                    .append("<a>" + item.label + "</a>")
                    .appendTo(ul);
        };

a combination of @Jörn Zaefferer and @Cheeso's responses.

Super helpful. Thank you. +1.

Here is a light version that sorts on "String must begin with the term":

function hackAutocomplete(){

    $.extend($.ui.autocomplete, {
        filter: function(array, term){
            var matcher = new RegExp("^" + term, "i");

            return $.grep(array, function(value){
                return matcher.test(value.label || value.value || value);
            });
        }
    });
}

hackAutocomplete();

for an even easier way, try this:

$('ul: li: a[class=ui-corner-all]').each (function (){      
 //grab each text value 
 var text1 = $(this).text();     
 //grab user input from the search box
 var val = $('#s').val()
     //convert 
 re = new RegExp(val, "ig") 
 //match with the converted value
 matchNew = text1.match(re);
 //Find the reg expression, replace it with blue coloring/
 text = text1.replace(matchNew, ("<span style='font-weight:bold;color:green;'>")  + matchNew +    ("</span>"));

    $(this).html(text)
});
  }

If you instead use the 3rd party plugin, it has a highlight option: http://docs.jquery.com/Plugins/Autocomplete/autocomplete#url_or_dataoptions

(see the Options tab)

Wouldn't such monkey patching apply to all instances of any autocomplete used on the page? If you have several, you'd often want different result rendering on each.

Take a look at the combobox demo, it includes result highlighting: http://jqueryui.com/demos/autocomplete/#combobox

The regex in use there also deals with html results.

Thanks Cheeso for the helpful monkey patch. Once little annoyance though - is there a way to make the replacement keep the case of the original text?

For example:- Typing 'c' will bring up '*c*alifornia'. Is there a way for it to show '*C*alifornia'? Similarly for letters appearing in the middle of phrases.

That would be really nice thanks!

Here is a version that does not require any regular expressions and matches multiple results in the label.

$.ui.autocomplete.prototype._renderItem = function (ul, item) {
            var highlighted = item.label.split(this.term).join('<strong>' + this.term +  '</strong>');
            return $("<li></li>")
                .data("item.autocomplete", item)
                .append("<a>" + highlighted + "</a>")
                .appendTo(ul);
};