Edit in JSFiddle

$(document).ready(function() {
    $('#stackable_autocomplete_field').keyup(function() {
        var $elem = $(this);
        var time = (new Date()).getTime();
        var $result = $('<div>', {
            id: time
        }).html('Requesting..').appendTo($elem.next());
        $.ajax({
            url: '/echo/js/',
            data: {
                js: '$(\'#' + time + '\').html(\'' + $elem.val() + '\');',
                delay: 2
            },
            type: 'GET'
        });
    });

    $('#non_stackable_autocomplete_field').keyup(function() {
        var $elem = $(this);
        var time = (new Date()).getTime();
        var $result = $('<div>', {
            id: time
        }).html('Requesting..').appendTo($elem.next());
        // abort existing previous request
        if ($elem.data('autocompleteAJAX')) {
            $elem.data('autocompleteAJAX').abort();
        }
        $(this).data('autocompleteAJAX', $.ajax({
            url: '/echo/js/',
            data: {
                js: '$(\'#' + time + '\').html(\'' + $elem.val() + '\');',
                delay: 2
            },
            type: 'GET',
            error: function(XMLHttpRequest, textStatus) {
                if (textStatus == 'abort') $result.html('Aborted');
            }
        }));
    });
});

<input type="text" id="stackable_autocomplete_field">
<div></div>
<input type="text" id="non_stackable_autocomplete_field"> 
<div></div>