What I'd really like is a single online notification service. I imagine signing up for a service somewhere, and I just plunk my special notification address somewhere in the settings. The service then communicates to that online notification service instead of sending me emails. I could install an app on my phone and desktop (separately configurable) that alerts me. I can set up filters through the app or a web interface.
I'm not too hopeful about this ever happening though. No service will support it unless it's mainstream, and using the notification service is useless until most services support it. Chicken and the egg.