jQuery get image's HTML as string

jQuery("#user-dialog .product-item img").get(0).outerHTML;

You're effectively looking for the outerHTML (in those browsers that support it):

var imageHtml = $("#user-dialog .product-item img").map(function(){
        return this.outerHTML;
    }).get();

JS Fiddle demo.

This will, of course, return an array of the img element's HTML; which allows jQuery to collate all the relevant information, rather than explicitly iterating through the matched set with get() or using bracket-notation indices [n]

And a simple (seriously, it's very simple) plugin to retrieve the outerHTML of the matched elements:

(function ($) {
    $.fn.htmlOuter = function () {
        var self = this,
            len = self.length,
            _tmp = document.createElement('div'),
            _h = [];
        for (var i = 0; i < len; i++) {
            _tmp.appendChild(self[i].cloneNode());
            _h.push(_tmp.innerHTML);
            _tmp.innerHTML = '';
        }

        return _h;
    };
})(jQuery);

var images = $('img').htmlOuter();
console.log(images);

JS Fiddle demo.

Note that the above returns an array, whereas, ordinarily, jQuery getters return results from only the first element of a matched set, if that's what you'd prefer then you could alter the final line of the plugin to:

return _h[0];

JS Fiddle demo.

Oh, and obviously (like .text() and other getter methods) this explitly cannot be chained, given that it returns an array, or a string (if you preferred), not the jQuery object.

References:

• jQuery:
  • get().
  • map().
• 'Plain' JavaScript:
  • Array.push().
  • document.createElement().
  • Node.appendChild().
  • Node.cloneNode().
  • outerHTML.
  • outerHTML compatibility.