I have an Asus that I need to reinstall Windows 8 on. It came with Windows 8 preinstalled but I do not have its recovery disc. Is it possible to use the recovery disc from a similar machine to install Windows? I'd like to use the product key from my machine.
There is no specific answer to this question.
It may possible to do as you suggest, but as to whether it will work or not, that will be determined by the restore package itself, and the choices made by the OEM.
Your Key should work as long as both the disk and the system are ASUS OEM licensed, but there is likely a model detection feature to their restore disks that may prevent you from installing it at all.
You may end up with drivers that are not right for your system. this issue will range in severity from critical to negligible, depending on how similar the two platforms really are. for instance make absolutely certain they use the same chipset. at least if your network card is functional you can download other drivers as needed.
New pcs today are delivered with no media BUT with an existing recovery tool whitch allows you to burn your windows 8 install media for that pc / notebook.
If you use a different media it could happen that the key dosent work or you are not able to activate the copy. If you are able to install with a different media you´re fine. If you cant activate after that just call microsoft activation hotline.