It's a good question because of the weight and width of the aircraft and for the sheer number of passengers involved.
My airline (and I'm sure other operators of the A380 have similar) has a list of suitable airports that consider not only the ability to land on the runway but also to vacate it, to park somewhere, to be able to refuel, to be able to disembark passengers, to be able to take off again. These airports are then classified in terms of suitability for diversion in different levels of urgency - problem at planned destination, medical emergency, serious technical problem, LAND ASAP. So Goose Bay for example is somewhere you would be unlikely to go if someone was ill, but if you have an engine that has discarded its entire front fan assembly and you cannot be sure whether there is secondary damage that could affect your ability to continue the flight then its a safe landing place.