UL
That's why those wall warts are so danged popular. It's the line voltage that is dangerous on an otherwise low-voltage device. Years ago, I read in one of the engineering magazines that UL approval was automatic if you made your product as a LV device and powered it with a wall wart. If the wal wart was UL approved, you were approved. Understand that this approval doesn't actually cover your device, but only the wall wart, but that's all that you're worried about. It takes time and money to get UL approval, so you let the wall wart company do all of that in one of their off-the-shelf products.
If, on the other hand, your device transforms the LV of the wart up to something lethal, then you may have other problems.
UL approval isn't mandatory unless you want to sell to certain markets. In many cases, CSA or the respective Euro approval is even more important to have if you plan to market there. My understanding is that you can't even sell non-approved items in Europe.
I'd suggest looking up information under Underwriter's Laboratories to see what should be approved, etc.
Dean