I recently purchased a new Macbook Air which obviously came with Mountain Lion. I am wondering if there is a way to download the installer for free onto another computer I have to create a re-install disk from, without having to pay the $20 to download from the Mac App Store.
You can download Apple's official OSX Recovery Disk assistant to create a flash drive with the capability to re-install OSX on an eligible Apple computer. A flash drive (it must be larger then 1GB) also enables you to easily re-install OSX on products such as the MacBook Air which don't have optical drives.
There is also a support document about the Recovery Disk Assistant.