Firefox only (Win/Mac/Linux): Firefox extension Yip adds notification support for web applications, even adding native Growl support for Mac users.
Adding the notifications to your browser is easy enough—just install Yip and you can test them out with the web-based Meebo instant messenger or Filttr for interacting with Twitter. Mac users will see a Growl popup, and Windows or Linux users should see the standard Firefox notifications dialog.
The really exciting feature, however, is the ability to create your own Greasemonkey scripts that enable notifications for your favourite website—you can already find scripts for Gmail, Facebook, Friendfeed and more—we tested the Meebo notifications that work right out of the box, but your results may vary on the user-contributed scripts. The author has written instructions on how to use the API, so if your favourite web application doesn't work yet, it might in the future.
Yip is free and open source, requires Firefox. For more, check out the FirefoxNotify extension for Ubuntu's new notifications system.