In addition to the ones that were already mentioned, I also care about:

Class announcements (currently emailed to me)

Reminders from my calendar (currently email or rss'd)

New posts from blogs I follow (currently RSS)

Notification of shared document changes (currently login to each service to check)

Private messages on forums (currently emailed)

E-mail, twitter, calendar invitations, meeting notifications, facebook messages, linkedin, text messages, voicemail, finance-related alerts, sports scores...