How can my app get a list of calendars on user's iPhone

Searching through the documentation reveals an EKEventStore class that has a calendars property.

My guess is that you'd do something like:

EKEventStore * eventStore = [[EKEventStore alloc] init];
NSArray * calendars = [eventStore calendars];

EDIT: As of iOS 6, you need to specify whether you want to retrieve calendars of reminders or calendars of events:

EKEventStore * eventStore = [[EKEventStore alloc] init];
EKEntityType type = // EKEntityTypeReminder or EKEntityTypeEvent
NSArray * calendars = [eventStore calendarsForEntityType:type];