Setting up longpolling
I can't say whether yours is right or wrong but there were a couple of things that seemed odd to me.

I wouldn't add functions to variables unless you intend to use them more than once. (or it adds to the readability)

var startAjaxing = function() {
    myajaxer = getAjaxer($("#myid"));
    myajaxer();
}

$(startAjaxing);


then becomes:

$(function() {
    getAjaxer($("#myid"))();
}); // Start ajaxing


Also I would get rid of arguments.callee and get the element every time:

var getAjaxer = null;
getAjaxer = function(elementid) {
    return function() {
        $.ajax({
            url: "/path/to/resource",
            success: function(response) {
                $("#" + elementid).html(response);
            },
            dataType: "html",
            timeout: 10000,
            type: "POST",
            complete: getAjaxer(elementid);
        });
    };
}


To ME this seems easier to read butt it may be only a matter of taste. (PS. I didn't check this for syntax errors etc.)

If you don't want to create functions every time?

getAjaxer = function(elementid) {
    var elementAjaxer = $("#" + elementid).data("ajaxer");
    if(elementAjaxer == null){
        elementAjaxer = function() {
            $.ajax({
            // etc etc
            });
        };
        $("#" + elementid).data("ajaxer", elementAjaxer);
    }
    return elementAjaxer;
}