As of January 1, 2009 Arizona requires that an Arizona license plate on a vehicle must be clearly visible, and that the word "Arizona" at the top of the plate may not be covered.
The wording of A.R.S. 28-2354 that is applicable here is:
A person shall display all license plates as required by subsection A until their lawful use expires or is canceled or revoked. A person shall maintain each license plate so it is clearly legible and so that the name of this state at the top of the license plate is not obscured.
The obvious target here is license plate frames that cover up parts of the plate. This does not apply to license plates from other states. Automobile dealerships are aware of the law, and should have redesigned their promotional license plate frames accordingly.
The high number of personalized plates in Arizona has apparently made it difficult for authorities to identify plates where parts of the plate may be obscured by frames. If you have a license plate frame on your vehicle that covers the word "Arizona" you are advised to remove it. The fine, depending on where you get pulled over, could be $150 or more.