At the end of the Season Three finale, The Last of the Time Lords, the Doctor and Captain Jack Harkness part ways for what could be the final time with Jack's rather strange decision to forego travelling through time and space to look after a bunch of jerks who refuse to trust him and actually tried to kill him. This more baffling because the immortal Jack could spend a few centuries travelling with the Doctor before heading back to Torchwood. What's more important is the final speech.
"But I keep wondering: what about aging? Cause, I can't die but I keep getting older. The odd little grey hair, you know. What happens if I live for a million years? ...OK, vanity, sorry, yeah, can't help it. Used to be a poster boy when I was a kid, living in the Boeshane Peninsula, tiny little place. 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."
He then laughs, points at the Doctor and Martha's shocked expressions and then says,
"I'll be seeing you," and heads off, leaving Martha to exclaim "He can't be!" and the Doctor, startled, to say, "No. Can't be. NO!" before starting to laugh.
Fans being fan looked at this scene and instantly came to the conclusion.
JACK IS THE FACE OF BOE!
Yet, RTD, the guy who wrote every last appearance of the Face of Boe, and all bar two episodes of Doctor Who's Captain Jack, was reluctant to confirm the obvious. Why? It's not some kind of long term plan since Jack's return to Doctor Who is highly, highly unlikely. Another series of Torchwood is similarly unlikely, since John Barrowman is so damned busy all the time.
RTD would only refuse to commit himself for two reasons: either Jack's story has more to be told (unlikely if he is the Face of Boe, in which case, that story is told), or else, quite simply, Jack is not the Face of Boe.
The TV series gives little information about what, at first, was nothing more than a prop mixing Arcturus from Curse of Peladon with the Severed Celebrity Heads of Futurama. We know he has been alive from before the year 200, 000 (where he was so famous he merited his own TV show despite the xenophobic human empire) and was pregnant with 'Boemina'. From the Silver Devastation, (apparently some location in the Isop Galaxy) the Face of Boe was rich enough to sponser the Earthdeath celebration, and got on well with the Moxx of Balhoun. The Face is the last of 'Boekind' 23 years later and is able to prevent his own death and teleport at will, send psychic messages through time and space, and his life force can power a whole city, and that he dies, speaking for the first time to the Doctor: "You Are Not Alone". If Jack is the Face of Boe, he could easily have worked out an acronym to clue the Doctor about the Master's survival (and as we know Jack has a respect for the timelines and could willingly fulfill this destiny - he might have started the legends int the first place).
From that, there is little that makes you think Captain Jack was really the Face of Boe. Bar perhaps referring to the Doctor as an old friend, and his knowledge of the Time Lords, there is no hint he is really an old companion. The Ninth Doctor could have, for example, bumped into the Face of Boe in The Long Game so it's possible that the Face's knowledge is down to a future encounter with the Doctor, albiet prior to the former's death. (Time travel, you know). Certainly, all the references to 'Boekind' show that there were other such creatures as the Face of Boe, though what form they took is unknown, so the idea that Jack simply aged into a giant head is unlikely, as is the idea he moved to the Isop Galaxy. The Face of Boe not so much as trying to flirt with Novice Hame also suggests the Face is not Jack as much as the fact the Doctor can happily spend time with the Face, but his every instinct is to run for the hills at the sight of the 'impossible' Jack.
Of course, five billion years is a hell of a long time, and Jack could have easily changed into a giant severed head and back a dozen times over. But it's just as possible that he didn't.
Supporting evidence from RTD's biography of the Face of Boe in Monsters and Villains adds to the idea that the immortal Jack is the undying Boe: the Face of Boe outlived its six offspring (which apparently lived for the normal Boekind lifespan of sixty years) and is described as 'the creature God forgot' because of Boe's unending lifespan. It also notes that the apparent life support systems the Face of Boe possesses doesn't actually keep the head alive and could easily have survived without it.
The Doctor knows the most about Captain Jack's status, and explains that Bad Wolf made him a permanent fact. He cannot die because the universe must have him alive (hence the way non-fatal injuries are not magically healed). It seems odd that this god like power would not prevent Jack's aging unless, of course, it's mild paranoia on Jack's part and he doesn't actually look any older. The Doctor's digs about plastic surgery are just that. Digs. The resurrection is permanent, yet in New Earth the Face of Boe is clearly capable of choosing to die, and in Gridlock dies for good, after all his life energy is spent - yet Jack, in a similar fix in Torchwood: End of Days, simply takes slightly normal than longer to recover. Unless an episode in Series Four shows the Face of Boe revived after the Doctor and Martha left, this is the real problem.
Unless we assume that during five billion years Jack discovered how to die but chose not to, changed his entire physical appearance and species, moved to the Isop Galaxy and then acted in a completely un-Jack like manner simply to preserve the time lines, it really looks unlikely. And he would only behave like that if he knew he was destined to become the Face of Boe.
After all, for a well-travelled man like Jack who accompanied the Doctor and Rose, it is quite reasonable for him to have either known about it before he joined the TARDIS, or from Rose or the Doctor. In Stealer of Dreams, Jack mentions a friend who once dressed up as the Face of Boe for a fancy dress party. Even if Jack is exaggerating or out and out lying (which is, after all, a major part of Stealer of Dreams) he must at least know that the Face of Boe is a giant severed head that the Doctor and Rose have met.
This leads to the problem of Jack. He's a self-confessed con man and also a compulsive name dropper and story teller. Torchwood as a series makes no sense unless its taken as read most of the team think he's joking/lying all the time, as Jack's very first scene in the series gives him a monologue that reveals he is a time-travelling spaceman who was once pregnant. Whether he's lying or not, the team automatically assume he's being frivolous. In Torchwood: Captain Jack Harkness we discover that the name he has used for centuries is not even his real name.
Jack is, thus, not a reliable source. Did he really grow up in the Boeshane Peninsula? Is there even such a place? If he was called the Face of Boe, it's quite possible the nickname was not flattering but insulting - ie, Jack had a big head, he was so full of himself. If Jack can happily lie to his own side and lead them into a suicide charge, he can quite easily claim that when he grow up he'll be the Face of Boe.
The only thing we can be sure of is that Jack knows about the Face of Boe, and his little speech was not said in blissful ignorance, but with the knowledge that it is just possible that Jack could turn out to be one of the most mysterious beings in the created universe.
So, why not simply say, "What if I turn out to be the Face of Boe?"
Well, as has been mentioned, Jack is a conman, and what's more saying goodbye to a man he's been in love with for the best part of two centuries. It seems far more credible that Jack would take one last chance to wind the Doctor up than his sudden militaristic chivalry. When he finishes the speech, he points at the Doctor as if to say, "Gotcha" and walks up where the Doctor laughs, and denies it. All it needed was for Jack to say "April Fool!" and the scene would be complete.
If Jack is not the Face of Boe, it raises a few questions, but are easily answered. If Jack is immortal and indestructible, then he could easily survive until the development of intergalactic travel, head to the Isop Galaxy, meet the Face of Boe and tell him all about "You are not alone" and start all the legends - indeed, one would expect immortals to meet up with each other, thanks to their shared interests. This does beg the question of what does happen to Jack. Is he on the ship to Utopia? Could he end up as one of the Toclafane (would his body be able to be changed without snapping back to its former state?)? Is he caught in one of those collapsing galaxies? He could be one of the Futurekind for that matter.
Until further information comes to light in Season Four, we can onlyt be sure that Jack was joking in his final scene with the Doctor - even if it turns out he is going to end up dying on New Earth. It's either a gag or a truly demented piece of irony, and only time will tell which is which.