I'm being billed on my account when I haven't made any purchases

The apps may be free to download, but some of them allow you to make in-app purchases within them to unlock extra features. You've checked the purchase history on your account (Store > View My Account, Store > View My Apple ID on iTunes 11, menu option on your computer's iTunes) or have any auto-renewing subscriptions ? If not and you haven't made any in-app purchased then you can contact iTunes support via this page : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption