After Jack Harkness was brought back to life by Bad Wolf Rose, he is unable to die, not even from old age. At the end of Last of the Time Lords, the Doctor comments on the fact that he doesn't know how Jack will look when he gets older.
Jack mentioned that he was once nicknamed the Face of Boe and from there looking back there are subtle hints which prove he is the Face of Boe:
Since the Doctor meets the Face of Boe further in the future, the Face of Boe, having been Jack, knew about Yana being the Master.
The Face of Boe has the distinction of being the oldest being in the universe, which fits with the side-effects of Jack's Immortality.
In Gridlock, the Face of Boe welcomed death. I remember Jack indicating at one point he was growing tired of not dying after having watched human history from 1869 after escaping Satellite 5.
However, with that said, the Face of Boe died, even though Jack can't die. However, not even the Doctor knew whether Jack could die of old age, so I am wondering: is there anything more concrete on whether Jack does become the Face of Boe?