The national football team of Niue has never scored a goal.
Niue is a small island nation in the South Pacific, with a population of 1,600. And their national football team has in fact only played two matches in its history - both in the 1983 South Pacific Games. It's not as if goals weren't scored in those matches, however. Niue lost 14 nil to Tahiti, and 19 nil to Papua New Guinea.
At this point you may be thinking, well, so what? It's a tiny nation with the population of a village. Of course their sports teams are going to get thrashed by far, far bigger countries like Tahiti or Papua New Guinea...
In May 2015, the national Rugby League team of Niue played South Africa. They won 48 - 4.