Marie Byrd Land and Bir Tawil Triangle are the only two land areas on Earth not claimed by any country.
Marie Byrd Land is a portion of Antarctica so remote that no country in the world bothered to claim it. It's the single largest unclaimed territory on Earth.
Bir Tawil Triangle likely has no owner because of some administrative snafu. First of all, despite of its name, it's not a triangle at all. In fact, it has a trapezoidal shape. In 1899, when the British drew the map between Egypt and Sudan, Bir Tawil was put in Sudan's territory (which Egypt accepted). However, in 1902, when Sudan drew its own map, it put Bir Tawil on the Egyptian side! So far, neither country bothered to lay claim to this patch of land.
It was no big loss, however, as Bir Tawil is full of sand and a whole lot of nothing.