I like the Google Calendar App. After integrating it into my website, I have a few feature requests that I believe would improve the app (easiest to hardest):
1) Have a setting where events can be displayed in either the user's current timezone, the calendar's timezone, or a set timezone. (Google calendars and calendar events already have timezones associated with them. It's a bit frustrating that I have to pick a timezone when users might not be in that timezone).
2) Have a setting where you could enable the user to toggle between views: agenda, month, and week. (Tabbed? Dropdown?).
3) Allow visitors/members to add events