<input type="text" id="field_results"/><br>

<input type="checkbox" value="1">1<br>
<input type="checkbox" value="2">2<br>
<input type="checkbox" value="3">3


$(document).ready(function(){
    $(":checkbox").on('click', function() {
        if($(':checkbox:checked')) {
            var fields = $(":checkbox").val();
            jQuery.each( fields, function( i, field ) {
               $('#field_results').val($('#field_results').val() + field.value + " ");
            });
        }
    });
});

$(document).ready(function(){
    $checks = $(":checkbox");
    $checks.on('click', function() {
        var string = $checks.filter(":checked").map(function(){
            return this.value;
        }).get().join(" ");
        $('#field_results').val(string);
    });
});

$(document).ready(function(){
    $("input:checkbox").click(function() {
        var output = "";
        $("input:checked").each(function() {
            output += $(this).val() + " ";
        });

        $("#field_results").val(output.trim());

    });
});

if($(':checkbox:checked')) {

var fields = $(":checkbox").val();

$(":checkbox").on('change', function() {
    var total = [];
    $(':checkbox:checked').each( function(){  //find the checked checkboxes and loop through them
        total.push(this.value); //add the values to the array
    });
    $('#field_results').val(total.join(" "));  //join the array
});

$(":checkbox").on('click', function () {
    var fields = '';
    $(":checkbox").each(function () {
        if (this.checked) {
            fields += $(this).val() + ' ';
        }
    });
    $('#field_results').val($.trim(fields));
});