When I heard of the Amulet of Kings in Oblivion, I wanted to learn more about it. I found out only the one with the dragon blood, also known as the Dragonborn, can wear it as Baurus said just after Emperor Uriel Septim VII was killed by the Mythic Dawn. I wondered if I could equip the amulet. I did, and it says it slips off your neck. But if I, or any other non-Dragonborn, were able to wear it, what else will happen? Would it give you a curse? Would you have power, or not? I want to know what happens if someone who has no dragon blood were to wear the Amulet of Kings.
As far as within the game; nothing. The Amulet of Kings given to you at various points along the main quest line is just a 'regular' amulet with a script that checks if the player is trying to equip it. There are even ways to obtain versions of the amulet that lack the script that the player can equip.
Lore-wise; The Amulet of Kings is just an amulet that can't be worn by those who lack 'Dragon Blood' in their veins (the specific requirements have been debated). Presumably it reacts to them the same way it does the player in Oblivion, it just slips from their neck. It has no known negative effects and is largely used as a sword-in-the-stone type test.
According to the wiki, the amulet only slips off someones neck. That is kind of weird, because I thought anything effective can happen to you, but it just slips off your neck. I understand now.