In the Doctor Who episode "The Last of the Time Lords," Captain Jack wonders what he will look like in a million years time. He also gave us this little gem: "When I was a kid, living in the Boeshane peninsula, I was the first one ever to be signed up for the Time Agency. They were so proud of me. The Face of Boe, they called me..."
It's possible this comment was a coincidence- he's called 'Bo', 'Boe' or 'Bow' face as a weird nickname which has nothing to do with the head in a tank we saw earlier in the series; or a joke- either by the writers to the audience, or by Captain Jack to the Doctor and Martha. If this is the case, we've got to wonder how it is that Jack knows about the Face of Boe, or at least how he knows that the Doctor knows the Face of Boe...
This leaves us with the question of: 'Is Captain Jack the face of Boe?', or the real question, 'Is Captain Jack destined to become a huge, sqidgy face in a tank?'. Hmm. Well, we already know he's been made immortal by Rose (see episode "The Parting Of The Ways"), so that would explain how he managed to live beyond the age of a billion... Kind-of. The question of how he becomes a huge face could be explained by some (slightly sketchy) science.
We age becuase our cells are dying. We tend to have a good thing going as long as we're young, but then our immune system goes kaput, skin cells go on an extended honeymoon with gravity and our grandchildren- or Doctor Who's- suddenly start dropping round with high hopes of being written into our wills.
Therefore, if Captain Jack wants to live beyond the age of 150, he's going to have to find something a bit stronger than an anti-wrinkle cream.
As we saw with Cassandra, staying alive- and "beautiful"- is not easy. After seven hundred and eight surgery operations, she had her brain put in a jar- seeings as the brain is arguably the most important part of the human body- and the last bits of her, erm, "body" stretched across a frame. It looks like she kept all 2-metres-square of skin (it is said that if you stretched all of a human's skin out like a towel it will be at least 2 metres square in length), and had her eyes and mouth left in the centre... for some reason. Must be that futuristic "beauty" rearing it's flat, skin-like head.
Other vital organs appear to have been discarded by the Lady Cassandra, such as the heart and lungs, alongside a digestive and nervous system. I honestly have no idea how she managed to survive without them. Perhaps they were all in the same jar as her brain, and I just failed to notice it, or maybe our modern Scientists are wrong, and all we need to survive is a man who will hold our squirty bottle of moisturiser every time we demand it. It would appear that Cassandra still has veins embedded in her skin, although I'm not sure if they're connected to a heart to pump them...
Back to the Face of Boe, and the question of "why the hell is he a giant face?!" Well, Captain Jack has admittedly always been one for style, and it certainly makes a good impression on your guests if you're a giant head. It makes it look like you have a giant brain, and if your sole purpose in life (even an overly-extended life) is to look wise, then that can certainly help your convincingness. Besides, who amongst us hasn't wanted to live out their golden years as a head in a tank? Despite this, it's possible Captain Jack became a head out of necessity- he, like Cassandra, went down the eight-hundred-and-something-stupid surgery route, and- rather than becoming a piece of skin shouting "Moisturise me! Moisturise me!!!" every five minutes, he became an enlarged version of a shrunken head. Maybe he did the sensible thing and kept all his organs in there, or maybe they're behind him, out-of-sight, plugged into a games control and playing plants vs zombies.
Of course, it's entirely possible that Captain Jack became a head against his will- one fan-theory mentions the headless monks from later series, and cites them as responsible for his decapitation.
As is so often suggested in other sci-fi franchises, radiation of the gamma, beta or otherwise harmful kind is rumoured to be able to alter DNA. It's not hard to imagine the sometimes stupid and often risky antics that Jack could get up to in his spare time, and if one of them happened to expose him to radiation? WHAM, he's just got zapped into a giant. What the heck he did with the rest of his body I have no idea. Donated it to medical science? A modern art installation called 'The Body of Boe'?
Another option is that the natural process of ageing turned Boe into an immobile blob. Maybe all humans would melt into an overly-huge head if we got past the age of one million? Perhaps the dude got so many wrinkles he seized up, only speaking with his mouth for special occasions such as telling the Doctor "You are not alone"- as he speaks telepathically, if at all, before his final appearance.
Whatever happened, it's safe to say that Captain Jack could be the Face of Boe... However weird his transformative period was.