By the time children today are old enough to die from natural causes, we'll have a cure for that.
At some point I think we will 'cure' cellular senescence. Then humans can stay physically in their prime, indefinitely. But there are other limits, like memory. Because memories require physical space, there is only room for a limited amount.
I think we can get past that either naturally, by overwriting old memories, or artificially, by augmenting memory with technology. Research is already looking at brain augmentation with electronics.
So what will be the ultimate limit? Or will humans achieve immortality?
Yes, at least for a natural life. Who knows what is possible with gene therapy.
All cells in the human body are programmed to die. When cells fail to self-terminate (called apoptosis) the result is that the DNA of the cell gets fragmented, which causes all sorts of nasty things to happen, like tumor growth.
Of course, our cells reproduce. There's a bit of a debate on if nerve cells can do this or not. If not, the human lifespan is limited by the functional life of its neurons. If they can, the lifespan is just a factor of the rate at which neurons can be created to replace dying ones.
All of the above is considered in a vacuum though. In reality there are numerous natural (and artificial) toxins in our environment. These toxins cause damage to the DNA in our cells before they undergo cell death, which means that the damaged DNA is sometimes passed on the the new cells, and so on down the line. Because there's no test environment free of these toxins, we will never get a number for true maximum lifespan of a human.
You can read more about this if you do a search for "free-radical theory of aging." Its super interesting.