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.<
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.