This is the solution I came up with. I've written a generic function to create a jQueryUI dialog box. If you want, you can use Matt's suggestion to override the default alert function: window.alert = alert2;

// 通用的自包含的jQueryUI替代浏览器默认的JavaScript alert方法。
// 唯一的先决条件是包含jQuery和jQueryUI
// 该方法自动创建/销毁容器div
// 参数：
//     message = 要显示的消息
//     title = 警告框上要显示的标题
//     buttonText = 关闭警告框的按钮上要显示的文本
function alert2(message, title, buttonText) {

    buttonText = (buttonText == undefined) ? "确定" : buttonText;
    title = (title == undefined) ? "页面提示：" : title;

    var div = $('<div>');
    div.html(message);
    div.attr('title', title);
    div.dialog({
        autoOpen: true,
        modal: true,
        draggable: false,
        resizable: false,
        buttons: [{
            text: buttonText,
            click: function () {
                $(this).dialog("close");
                div.remove();
            }
        }]
    });
}

You can override an existing alert function that exists on the window object:

window.alert = function (message) {
  // 对消息进行处理
};