Non-jQuery version:

var parseXml;

if (window.DOMParser) {
    parseXml = function(xmlStr) {
        return ( new window.DOMParser() ).parseFromString(xmlStr, "text/xml");
    };
} else if (typeof window.ActiveXObject != "undefined" && new window.ActiveXObject("Microsoft.XMLDOM")) {
    parseXml = function(xmlStr) {
        var xmlDoc = new window.ActiveXObject("Microsoft.XMLDOM");
        xmlDoc.async = "false";
        xmlDoc.loadXML(xmlStr);
        return xmlDoc;
    };
} else {
    parseXml = function() { return null; }
}

var xmlDoc = parseXml("<foo>Stuff</foo>");
if (xmlDoc) {
    window.alert(xmlDoc.documentElement.nodeName);
}

Since jQuery 1.5, you can use jQuery.parseXML(), which works in exactly the same way as the above code:

var xmlDoc = jQuery.parseXML("<foo>Stuff</foo>");
if (xmlDoc) {
    window.alert(xmlDoc.documentElement.nodeName);
}

Wrap it in a jQuery object. Then use jQuery's normal DOM manipulation methods on it.

var t = $('<foo><bar>something</bar></foo>');

//loop over 'bar' nodes
t.find('bar').each(function () {
    alert($(this).text());
});

If you want to convert it back to a plain string (after modifying it for example) you can do it like so:

//then convert it back to a string
//for IE 
if (window.ActiveXObject) {
    var str = t.xml;
    alert(str);
 }
// code for Mozilla, Firefox, Opera, etc.
else {
   var str = (new XMLSerializer()).serializeToString(t);
   alert(str);
}

EDIT: The $.ajax manual says (on the processData option):

By default, data passed in to the data option as an object (technically, anything other than a string) will be processed and transformed into a query string, fitting to the default content-type "application/x-www-form-urlencoded". If you want to send DOMDocuments, or other non-processed data, set this option to false.

So if you're passing a jQuery object to the server, you'll need to set that to true, or omit it altogether (it is set to true by default). Hope that helped.

Yes, it is possible to convert a string into an XML. You need to use the DOMParser Class. Try something like this to convert:

let parser = new DOMParser();
let xml = parser.parseFromString( escaped, "text/xml");

Updated answer for 2017

The following will parse an XML string into an XML document in all major browsers. Unless you need support for IE <= 8 or some obscure browser, you could use the following function:

function parseXml(xmlStr) {
   return new window.DOMParser().parseFromString(xmlStr, "text/xml");
}

If you need to support IE <= 8, the following will do the job:

var parseXml;

if (typeof window.DOMParser != "undefined") {
    parseXml = function(xmlStr) {
        return new window.DOMParser().parseFromString(xmlStr, "text/xml");
    };
} else if (typeof window.ActiveXObject != "undefined" &&
       new window.ActiveXObject("Microsoft.XMLDOM")) {
    parseXml = function(xmlStr) {
        var xmlDoc = new window.ActiveXObject("Microsoft.XMLDOM");
        xmlDoc.async = "false";
        xmlDoc.loadXML(xmlStr);
        return xmlDoc;
    };
} else {
    throw new Error("No XML parser found");
}

Once you have a Document obtained via parseXml, you can use the usual DOM traversal methods/properties such as childNodes and getElementsByTagName() to get the nodes you want.

Example usage:

var xml = parseXml("<foo>Stuff</foo>");
alert(xml.documentElement.nodeName);

If you're using jQuery, from version 1.5 you can use its built-in parseXML() method, which is functionally identical to the function above.

var xml = $.parseXML("<foo>Stuff</foo>");
alert(xml.documentElement.nodeName);

You haven't told us how you go about displaying that object. XMLSerializer works on DOM nodes, so your object has to be added somewhere, for example:

document.getElementById('SomeDiv').appendChild(xml); 

and if you just want the full xml string to be displayed:

var xmlText = new XMLSerializer().serializeToString(xml);
var xmlTextNode = document.createTextNode(xmlText);
var parentDiv = document.getElementById('SomeDiv');
parentDiv.appendChild(xmlTextNode);