If the game is shown as "free" in the App Store, it is completely free to download, but many apps have "in-app purchases" intended to separate you from your money.
The solution is simple - don't use those apps. Uninstall them and write a review in the App Store explaining their underhandedness.
To disable "in-app purchases" go to Settings > General > Restrictions and turn "In-App Purchases" off. Don't forget your Restrictions passcode.