Many calendaring programs (Outlook, iCal) support vCal for downloading event information and adding it to your calendar. Others can use the vCalendar microformat to extract data. Neither of these, however, seems to be supported on the iPhone.
Is there any functional equivalent that will allow me to list event information on a page and have a website visitor add the event to her calendar with a single click? Since Mobile Safari makes it super-easy to extract emails and phone numbers from web pages, it seems odd that there's no similar functionality for events.
Update:
Note that this is a very old answer. Since iOS 5 you can use EKEventStore to access calendar events and Mobile Safari will open .ics files in Calendar.
Original Answer
It's not possible, there is no API for the calendar on the iPhone, sadly. You can build an app that registers for the ical URL scheme, but you still won't be able to save the calendar entries to the calendar backend since there is no API (like e.g. for the AddressBook).