How to remove close button on the jQuery UI dialog?

the "best" answer will not be good for multiple dialogs. here is a better solution.

open: function(event, ui) { 
    //hide close button.
    $(this).parent().children().children('.ui-dialog-titlebar-close').hide();
},

You can use CSS to hide the close button instead of JavaScript:

.ui-dialog-titlebar-close{
    display: none;
}

If you don't want to affect all the modals, you could use a rule like

.hide-close-btn .ui-dialog-titlebar-close{
    display: none;
}

And apply .hide-close-btn to the top node of the dialog

I have found this worked in the end (note the third line overriding the open function which find the button and hides it):

$("#div2").dialog({
    closeOnEscape: false,
    open: function(event, ui) {
        $(".ui-dialog-titlebar-close", ui.dialog || ui).hide();
    }
});

To hide the close button on all dialogs you can use the following CSS too:

.ui-dialog-titlebar-close {
    visibility: hidden;
}

Here is another option just using CSS that does not over ride every dialog on the page.

The CSS

.no-close .ui-dialog-titlebar-close {display: none }

The HTML

<div class="selector" title="No close button">
    This is a test without a close button
</div>

The Javascript.

$( ".selector" ).dialog({ dialogClass: 'no-close' });

Working Example