What will happen to our Mac if using higher RAM than Apple "allows" it? I am thinking to upgrade my RAM to be 16GB. However Apple states up to 8GB only.

Anyone has experience upgraded RAM more than Apple allows?
The MacBook Pro (Early 2011) support up to 16 GB of RAM just fine. Apple stated 8 GB of RAM as maximum when the model was released, but it has later been confirmed that it actually support 16 GB of RAM without problems. For example check this link:

MacBook Pro Early 2011 - EveryMac

The Mid 2010 and Mid 2012 Mac Pro's support at least 48 GB of RAM.

So all in all, there should be no problems in upgrading to 16 GB of RAM if you have one of these Mac models.