Most likely because Notification Center is a relatively new feature, Apple didn't necessarily want to push a whole new paradigm for clearing notifications. So instead, they multi-purposed [[UIApplication sharedApplication] setApplicationIconBadgeNumber: 0]; to clear said notifications. It might seem a bit weird, and Apple might provide a more intuitive way to do this in the future, but for the time being it's the official way.

Myself, I use this snippet:

[[UIApplication sharedApplication] setApplicationIconBadgeNumber: 0];
[[UIApplication sharedApplication] cancelAllLocalNotifications];

which never fails to clear all of the app's notifications from Notification Center.

Just to expand on pcperini's answer. As he mentions you will need to add the following code to your application:didFinishLaunchingWithOptions: method;

[[UIApplication sharedApplication] setApplicationIconBadgeNumber: 0];
[[UIApplication sharedApplication] cancelAllLocalNotifications];

You Also need to increment then decrement the badge in your application:didReceiveRemoteNotification: method if you are trying to clear the message from the message centre so that when a user enters you app from pressing a notification the message centre will also clear, ie;

[[UIApplication sharedApplication] setApplicationIconBadgeNumber: 1];
[[UIApplication sharedApplication] setApplicationIconBadgeNumber: 0];
[[UIApplication sharedApplication] cancelAllLocalNotifications];

It might also make sense to add a call to clearNotifications in applicationDidBecomeActive so that in case the application is in the background and comes back it will also clear the notifications.

- (void)applicationDidBecomeActive:(UIApplication *)application
{
[self clearNotifications];
}

Maybe in case there are scheduled alarms and uncleared app icon badges.

NSArray *scheduledLocalNotifications = [application scheduledLocalNotifications];
NSInteger applicationIconBadgeNumber = [application applicationIconBadgeNumber];


[application cancelAllLocalNotifications];
[application setApplicationIconBadgeNumber:0];


for (UILocalNotification* scheduledLocalNotification in scheduledLocalNotifications) {
[application scheduleLocalNotification:scheduledLocalNotification];
}
[application setApplicationIconBadgeNumber:applicationIconBadgeNumber];

If you have pending scheduled local notifications and don't want to use cancelAllLocalNotifications to clear old ones in Notification Center, you can also do the following:

[UIApplication sharedApplication].scheduledLocalNotifications = [UIApplication sharedApplication].scheduledLocalNotifications;

It appears that if you set the scheduledLocalNotifications it clears the old ones in Notification Center, and by setting it to itself, you retain the pending local notifications.

Got it from here. It works for iOS 9

UIApplication *app = [UIApplication sharedApplication];
NSArray *eventArray = [app scheduledLocalNotifications];
for (int i=0; i<[eventArray count]; i++)
{
UILocalNotification* oneEvent = [eventArray objectAtIndex:i];
//Cancelling local notification
[app cancelLocalNotification:oneEvent];
}

If you're coming here wondering the opposite (as I was), this post may be for you.

I couldn't figure out why my notifications were clearing when I cleared the badge...I manually increment the badge and then want to clear it when the user enters the app. That's no reason to clear out the notification center, though; they may still want to see or act on those notifications.

Negative 1 does the trick, luckily:

[UIApplication sharedApplication].applicationIconBadgeNumber = -1;

In Swift I'm using the following code inside my AppDelegate:

func applicationDidBecomeActive(application: UIApplication) {
application.applicationIconBadgeNumber = 0
application.cancelAllLocalNotifications()
}

When you have repeated notifications at future, you do not want to cancel those notifications, you can clear the item in notification center by:

func clearNotificationCenter() {
UIApplication.sharedApplication().applicationIconBadgeNumber = 1
UIApplication.sharedApplication().applicationIconBadgeNumber = 0
}

You cannot clear notification when your app is open in the foreground by calling the method below immediately after receiving local notification, otherwise you will receive tens of hundreds of notifications. Maybe because the same notification apply again, and now is the time to fire, so you keep fire, apply again, fire, apply....:

[UIApplication sharedApplication].scheduledLocalNotifications = [UIApplication sharedApplication].scheduledLocalNotifications;

When you logout from your app, at that time you have to use a below line of code on your logout button click method.

[[UIApplication sharedApplication] setApplicationIconBadgeNumber: 0];


[[UIApplication sharedApplication] cancelAllLocalNotifications];

and this works perfectly in my app.

Update for iOS 10 (Swift 3)

In order to clear all local notifications in iOS 10 apps, you should use the following code:

import UserNotifications


...


if #available(iOS 10.0, *) {
let center = UNUserNotificationCenter.current()
center.removeAllPendingNotificationRequests() // To remove all pending notifications which are not delivered yet but scheduled.
center.removeAllDeliveredNotifications() // To remove all delivered notifications
} else {
UIApplication.shared.cancelAllLocalNotifications()
}

This code handles the clearing of local notifications for iOS 10.x and all preceding versions of iOS. You will need to import UserNotifications for the iOS 10.x code.

You need to add below code in your AppDelegate applicationDidBecomeActive method.

[[UIApplication sharedApplication] setApplicationIconBadgeNumber: 0];