Assuming that we count speciation among humans as still being human then:
If we keep going the way we are without progress? The last man will die of some affliction that stems from the damage we caused to our world either via war or seriously poor judgement (much of a muchness). Too many possibilities to be specific.
If we can transcend our petty issues of today and step into tomorrow, then the next potential issue is something major affecting our ecosystem on earth like a major natural event (theorised "super volcanoes" can basically cover the earth in a cloud of ash, drastically decreasing sunlight and affecting all life at the most important of stages (photosynthesis)... the knock on affect could lead to our demise, which would either be malnutrition or toxicity (if the plummeting tempratures don't get us first).
Alternatively, it could an extraterrestrial event like an asteroid or an unprecedented blast of radiation from our sun.
If we are lucky and none of that happens, or if does happens and we manage to survive, the next big issue would be our sun dying and effectively making our solar system inhospitable. If we are still on earth, the sun will cool significantly first and we might freeze or when it expands into a Red Giant we might end of frying due to radiation if not actually be engulfed by the suns increased diameter.
If we have managed to move past our lonely little world into space and beyond then we could potentially escape that death. Its so far down the line, that if we ARE still here then we might not even need a homeworld to live off of, making us a Nomadic space faring species. Either that or we settle on other planets, though we would likely strip mine most planets for resources if we haven't learned to synthesis what we need from the loose atoms floating in space or from the stars themselves.
At this point chances are we will experience huge and multiple divergences in our species, especially if we settle on different planets with varying environmental influences.
From there, all I can imagine is that the last man will cease to be at the end of the universe.
And if we manage to survive that I can't fathom what would end us.