How do I cancel payment on an app processed by mistake?

If you got an email receipt, use the 'Report a Problem' link in it. Otherwise, click here and ask the iTunes Store staff for a refund.

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Just to be clear, you can’t cancel a payment for an app. As soon as you agree to download it, and it downloads, you are charged for the app right away. You can request a refund as described by Niel in his post above.