(I Am Not A Lawyer. This is my interpretation of the EULAs Microsoft have released on their website, and may not be legally sound. Additionally, the online EULA I reference may not match the specific terms you agree to; please read the licence terms included with your copy.)
Note: this answer applies for Windows 8 only. Windows 8.1 and newer got rid of the Personal Use Licence and moved back to a full retail channel.
Ok, let's clarify things. Hopefully for the last time.
There are two licences:
There are additional licences distributed by large OEMs that have their own contracts with Microsoft, such as Dell, HP, Lenovo, etc.. Those remain more or less the same and will not be covered by this answer. As long as you buy the licence/disk separate from the computer, it is under Personal Use, not OEM.
Traditionally, there was a System Builder licence used by OEMs (typically smaller shops, since large manufacturers tend to have their own contracts). And then there was a full retail licence used by home users. What has been reported is that the removal of the retail licence, 'forcing' users to use the OEM licence with all its restrictions. This is incorrect.
Yes, the traditional 'retail licence' has been removed. Yes, home users must now buy a System Builder licence. No, that is not an OEM licence (practically speaking). Home users who purchase a copy of Windows 8 separate from their computer fall under the Personal Use section of the System Builder licence, which is more or less the same as the traditional 'retail' licence. It just got renamed and consolidated with the OEM licence into one package/price. You still have the same right to support from Microsoft and right to transfer the licence you would have had on the traditional retail licence.1
Now, to address the misconception that the System Builder licence is an OEM licence. For all intents and purposes, it is not. For previous versions of Windows, yes, but not for Windows 8.
Now, firstly, if you were to look at the System Builder licence you would find it here. That is the OEM licensing page. Disconcerting, yes?
However, if you actually read the licence, it states:
If you are not a system builder and are installing this product for personal use, refer to www.windows.com/personaluselicense for terms that apply to you
So, the OEM part of the licence only applies to OEMs! What a surprise!
Now, on to the personal use licence. This is the equivalent of the traditional retail licence, both in terms and in spirit. There are several parts that were part of Windows 7's retail licence, but not OEM, that are in here:
Let me reiterate. The Personal Use licence is practically the same as the traditional retail licence. It is not an OEM licence.
1(Note: the support is described as 'limited' in the EULA, and apparently there is a message on the box saying there is no support. See the comments under this answer for further details.)
According to Microsoft, an Windows 8 Key provided from am OEM is not transferrable:
Q: My customer bought a new PC and wants to move the OEM software from the old PC to the new one. Can't users do whatever they want with their software?
A: No, the OEM software is licensed with the computer system on which it was originally installed and is tied to that original machine. OEM licenses are single-use licenses that cannot be installed on more than one computer system, even if the original machine is no longer in use. The End User Software License Terms, which the end user must accept before using the software, state that the license may not be shared, transferred to, or used concurrently on different computers
Reference
That's the legalese behind it. As far as technically, can you do it, Windows 8 OEM licenses seem to be tied to hardware hashes that include the motherboard:
manufacturers will be required to write a unique Windows product key -- which is associated with the hardware hash -- into the system's BIOS
Reference
So no, it would appear that even with the original OEM key and installation media, the key is bound to the hardware it is installed on.
Best Answer
Rather than discuss something I don't know or understand like many of the poster's above (who seem to be leveraging former experiences with prior OSes) I will state my experience and you can accept it for it is.
I purchased an ACER M5 with a pre-loaded OEM version of windows 8, similarly there was no affixed sticker stating the product key. I removed the original hard drive and upgraded to a new SSD. No efforts towards imaging or maintaining of the original HHD were performed. I purchased a system builders DVD for windows 8 pro to install onto the new, entirely blank SSD. During the installation, I was never asked to input a product key. My final istallation was a copy of windows 8 (non pro). Futhermore, a check on the last 5 digits of the product key applied on my installation reflected a different product key than the one shipped with the system builder DVD.
Speculation: the OEM product key was stored elsewhere on the machine, detected, and employed rather than asking the user to supply a product key. I've read elsewhere that the key is maintained in the BIOS for new OEMs from major PC manufactures to simplify reporting to Microsoft.
Personal: I build a new box every two years so the fact that my product key was never requested doesn't impact me; my purchased personal use license for W8 pro will be used eventually.