How do you restore the OS without restoration disks? Recently got a new macbook pro as an upgrade from an older macbook(white). I remember that there were restoration disks containing the installed OS in the packaging with the older machine. However, with the new machine there were no disks or any other storage media.

In the future, if I needed to reinstall the OS, would I be forced to buy another copy from the App Store?
No, you do not have to purchase OS X more than once.
If you are referring to OS X Lion and Mountain Lion, both of which were distributed from the App Store, one purchase is enough for every Mac that you own or control.  (see Apple's EULA for this) Additionally, Lion and Mountain Lion have Internet Recovery, which means that a drive that fails or any new drive installed without OS X will be automatically connected to the Internet and installed with a fresh copy of your respective OS.
Additionally, Apple has their own Recovery Disk Assistant for making USB drives for physical media recovery solutions, or you can use LionDiskMaker. Make sure to read LionDiskMaker's FAQ (in the link provided),  as this answers crucial questions concerning the application's usage.