Facebook Desktop brings every notification to Windows and Mac and Linux!
Still, Facebook Desktop works. Beyond notifications, it also lets you publish status updates -- but as you have to go via a tiny system tray icon, and there's no way to set a global hotkey, it's probably easier to just pop open a browser window and update your status normally.
The only problem -- for some people, anyway -- is that Facebook Desktop is an Adobe AIR app. It's advertised as "lightweight", but a 45MB memory footprint for an app that pops up toast windows seems a little on the chunky side. By default it loads on computer start-up, too, which is a bit obnoxious -- you can disable that in the settings, though.
Oh, it also requests a truly insane number of permissions when connecting to your Facebook account (picture after the break). Understandably, it needs to check a lot of things, but it doesn't need permission to publish check-ins, or insight data for my Pages. Heck, why does it even need my name, profile picture and gender?