The W3C started in 2010 a working group to implement notifications:
http://www.w3.org/2010/web-notifications/
This Working Group develops APIs that expose those mechanisms to Web Applications—so that Web developers creating, for example, Web-based e-mail clients and instant-messaging clients can more closely integrate their Web application behavior with the notification features of the operating systems of their end users.
Finally the result is like a bad joke as it works only if the specific website is open:
http://alxgbsn.co.uk/notify.js/
I think they missed to implement the possibility to add push urls so the browser is able to ask for notifications while its running in the background - and above all - if all tabs have been closed.