The answer to this question is "now". At this moment Bir Tawil is unclaimed by any country. It is on the border between Egypt and Sudan. Both Egypt and Sudan claim a larger piece of land closer to the Red Sea, and both consider Bir Tawil to belong to the other country.

[Note this is one example of unclaimed land; there may be others though I'm not immediately aware of any. This one example answers your question though.]

There are still pieces of land left unclaimed. Apart from Bir Tawil as /u/edXcitizen87539319 has just said, there is also a large tract of Antarctica that was never claimed by any sovereign nation. In fact, nder the Antarctic Treaty, all present claims on Antarctic land are unrecognised.

Follow-up: Disregarding the 2 currently unclaimed pieces of land (Bir Tawil and Marie Byrd Land), what was the last piece of territory to be claimed?

In addition to what has already been mentioned, there is some land along the Danube rover in Eastern Europe that are unclaimed due to a border dispute between Croatia and Serbia: http://en.m.wikipedia.org/wiki/Croatia–Serbia_border_dispute

Also, the vast majority of the land on Earth is unclaimed because it is covered with salt water. If it breaks the surface due to geological processes then it is claimed almost immediately.

In addition, celestial bodies have not been claimed by any country, although this could be a potential source of future conflict.