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Google Calendar (by Google)
I rely extensively on Google Calendar. I don't just use it to manage appointments, I use it to manage my time, so I know when I have time for projects and when my time has been allocated. Google Calendar has become one of my mission-critical tools.
The Google Calendar extension gives a quick look inside Google Calendar. For me, it's helpful to quickly see if I have something coming up, but not as helpful for managing projects.
How often used: A few times a week, when I don't want to open a whole calendar Web page.
Live without it factor: I could live without it, but I'd prefer not too.