The iPhone has a setting which can enable Islamic, Hebrew and Chinese calendars in the built in calendar app. It's called alternate calendars and can be enabled from the settings app.
To do so: Open Settings --> Mail, Contacts & Calendars (scroll down to the bottom) --> Alternate Calendars. Then pick the alternate calendar that you would like to enable. You can only have one picked at a time.
The result is a well integrated alternate calendar for your iPhone. Enabling alternate calendars will show the dates in the calendar app as well as the Today view in the Notification Center.
This is pretty useful, for example for Muslims to see what the Hijri date is. And it's even more useful during Ramadan. Users selecting Chinese or Hebrew alternate calendars may also find it useful to enable those calendars.