Apple has begun their iPhone 4 case program as promised and all of the information is on this page.
The policy is as follows:
If you purchase an iPhone 4 before September 30th, 2010, you are eligible to receive an iPhone 4 Bumper or a select third-party case from Apple at no charge.
For new purchases follow these steps to apply for a Bumper or case
1. Download the iPhone 4 Case Program app from the App Store HERE.
2. Launch the app on your iPhone 4 and sign in using your iTunes Store account or Apple ID.
3. Select your Bumper or case. For iPhone 4 purchases made before July 23rd, 2010, you must apply no later than August 22nd, 2010; otherwise, you must apply within 30 days of your iPhone 4 purchase. To qualify for this program, you must purchase your iPhone 4 by September 30th, 2010.
If you already bought a case from Apple they will give you a full refund for your previously purchased iPhone 4 Bumper, including any taxes and shipping fees.
Prior credit card purchases
Apple has already refunded your account. It may take up to one billing cycle for the refund to appear. Apple Retail Store customers can check the status of your refund HERE.
Cash, check, or gift card at an Apple Retail Store
Return to the store with your receipt by September 30, 2010, to get your refund.
Gift card on the Apple Online Store
Apple will automatically mail you a new gift card for the refund amount.
If you bought from an AT&T Store
Apple will reimburse you for the purchase price of your iPhone 4 Bumper. Just fill out this rebate coupon and mail it to Apple by September 30th, 2010. You will be sent your rebate as soon as your claim is processed.