I know W3C just publish their draft version of Web Notification to notify user. So, there is no browser that implement this method in their current or latest build browser.<
These are some that I found:
I doubt that there are any cross-browser desktop notification javascript libraries, because those notifications are vendor specific implementations, made by the web browsers themselves, and not the W3C or WHATWG.
CreatePopup looks like it was made for enterprise web applications as it never took prominence, and Google wants web applications to replace desktop applications. Jumplists are just a way to provide Windows 7 functionality into IE9, but it's not a move to push to cloud computing.
I know this is old but Push.js allows for cross-browser desktop notification.
Also, this is 2020, you can use the native Notification API in most browsers.
Make sure you check the Browser compatibility section.
I don't know of a cross-browser lib; but desktop-notifications are coming to Mozilla Firefox post 4.0 as well. They're implemented in trunk already: https://bugzilla.mozilla.org/show_bug.cgi?id=573588
Though apparently this new feature won't get included in FF 4.0: https://bugzilla.mozilla.org/show_bug.cgi?id=594543
But in the long term, an api related to but different from the webkit will be available.
Not sure about opera, however.
The dojo toolkit http://www.dojotoolkit.org contains a control called "Toaster" in its dojox package, but this is a notification inside the browser window and does not follow the web notifications specification. Maybe it is also a solution for your webapp.