You can set up a web-based calendar system by clicking on the Calendar link in the upper left corner of the Gmail page.
You can set up multiple calendars. They can be private or available to anyone out on the Web.
My wife and I share our calendars and I have set up a community calendar that the members of our church use.
You can synch a Google calendar with your own calendar system including your iPhone, BlackBerry, or Android phone.
On the Calendar page click on the Gear icon (upper right corner) and then select "Settings"