I've written a step by step tutorial with screenshots for those that want to create a SG iTunes Account so that you can download the Free Case Program App. You still need a Singapore address and someone from there to send you the case.
1. Open iTunes on your computer
On the right hand panel called Quick Links - click Change Country


2. Select the Country of your choice
A bunch of flags will appear and you select Singapore (or another country where you want the case send to - but not Malaysia)

3. Browse for the Free Bumper Case and Create an Account
Once you have selected the country, it will go back to the iTunes Store. At the top right hand corner, type Free Bumper Case into the search box
Now the iPhone app will appear and you click on it and a box will appear to ask you to log on to your account or create an account. Click Create New Account. You can also select any other Free Apps for the same purpose. (see right panel at the middle)

4. Welcome to the iTunes Store
A welcome screen will appear - you click Continue

5. iTunes Store Terms & Condition
Check the box at the bottom of the T&C and click Continue

6. Create an Apple ID
Put in your own email address. This must be a valid email address. You can't use any email address which you had previously used before.
Fill out the rest - a password (remember to write this down for later), question and answer, your date of birth. Click Continue when done.

7. Provide a Payment Method.
Ok on this screen, you select None then fill in the name and address. Since you are only creating this account for the sole purpose of getting the free case, I suggest that you fill in the name and address of your friend who will be receiving the case for you. For town you put Singapore. The phone number area code you put 65.

8. Verify Your Account.
This page you just click Done.
An email will then be send to the address you entered above. Click "Verify Now" on your email. It will open a new page for you to enter your email address (Apple ID) and your password. Once it says Verified, we can go to the next step. The Apple ID verification server might take many tries before it can load the page. Try again if it fails the load the verification page.

9. Download the App into your iPhone
Go to Settings > App Store (scroll down to see it)
Click Sign In. (if you are already signed in to your MY account - sign out first). Now sign in with the email address that you created above.
Once you signed in, press your Home button to exit. Then select App Store, and click Search at the bottom and type Free Bumper Case in the search box above. The app should appear and you download that.
10. Order your free case
Click on the iPhone 4 Case Program App and follow the instructions to order your case. The shipping address will be already filled out but you can amend this incase you want to send it somewhere else. You will get an Order Acknowledgement email once this is done. Also remember to sign out of this account and sign back into your MY account when all is done.

Good Luck !!!