In web application it is some what difficult task. because you rarely see a web application manipulating a windows task.
If you note, the notifications coming from gtalk and yahoo messenger are coming because you have installed an application for that.
That G-talk or Yahoo messenger software act a bridge between the web server and your windows. Normally in a web application there is web server and browser so results are returned to your browser only not to the windows.
To accomplish what you want to do, you have to create a simple exe file ie. a windows application which runs in background or something and let that application communicate with your web server and then process and give a pop up notification.
NOTE : If this thing was so easy then you would have seen facebook notifications poping up through your task bar.