There is no way to remove a specific notification as of iOS SDK 5.0. The way to remove all the notifications from your app so they don’t show in the Notification Center when the user opens the app from one of them, is to set the app badge to 0, like this:
[UIApplication sharedApplication].applicationIconBadgeNumber = 0;
EDIT: on iOS 8, SpringBoard seems to be automatically dismissing a notification when you tap on it on the Notification Center to open the app.