The X series ostensively takes place in the future of the original series. But just who is X? Believe it or not, we don’t officially know, because Capcom has never said.
It is in my opinion—though I could be wrong—that X is not Mega Man or any other robot in existence, but instead a totally new and original creation, built from scratch. Why? Well, think of it this way. We already know that this is the case with Zero—Zero can’t be a rebuilt Proto Man, Bass, or any other character currently existing in the Mega Man series because Dr. Wily has been building Zero since the Power Battle (which seems to occur just after Mega Man 7). Now, here’s the key—if Zero is indeed copied off plans of Dr. Light’s, then X as well must already exist or Dr. Wily would have no plans to copy. So this rules out Mega Man being X just as it rules out anyone being Zero. Of course, if Zero has no relation to X, then X’s identity is still under debate; however, it does make you wonder why Zero and X are so similar. I suppose we’ll just have to wait and see.
Plot Holes
On related note, I find it curious that there’s almost no mention of the original series in the X series. Oh, you hear about Dr. Light and Dr. Wily, but ever notice that none of the characters in the X series ever mention anyone else? You’d think if the X series was the future of the original, then Mega Man and Dr. Wily at least would have made a mark on history. You’d think people would wonder about the fact that Mega Man X is incredibly similar to Mega Man (even going so far as to share the same name and the same creator). You’d think people would talk about the previous Wily wars and why no one learned from their past mistakes.
But curiously, no mention of any of these is made in the X series. We see mentions of Dr. Light and Dr. Wily, but it’s as if Mega Man himself never lived. And it’s as if Dr. Wily never once tried to take over the world. As if none of that had ever happened. You suppose everyone on the planet has hideous, global amnesia? (And just what happened to all of their books, CDs, DVDs, hard drives, tape backups, video cassettes, and so forth filled with their own history? How is it that no one on the planet knows what happened in the past hundred or so years?)
This almost leads to the conclusion that the X series isn’t really the future of the original at all, even though that’s clearly what Capcom intended. Look at it from another angle. Dr. Light wrote on X’s capsule that X was capable of thinking and feeling emotions and such...yet all of the robots in the original series have been able to do that since at least by the time of Mega Man 8 or so, probably earlier. Just take a look at any number of Capcom’s more recent games, such as Battle & Chase or Super Adventure. Heck, even the Mets in Super Adventure seem to have thoughts and emotions.
And, to top it off, just look at Mega Man 9. The Robot Masters in that game willingly rebel. If that doesn’t completely blow the plot of the X series out of the water, I don’t know what would.
So if all of the robots in Dr. Light’s time could do that anyway, why would Dr. Light write what he did on X’s capsule like it was some new and unusual thing? The only explanation that fits is that all of the original series robots didn’t exist in the X series world, and that X was Dr. Light’s first truly great creation...which would mean that Dr. Light never made Mega Man in the X series time line. Which would mean the X series isn’t really the future of the original at all.
Oh, I’m fully aware that Capcom meant for the X series to be the future of the original. But they’ve certainly filled that plot with plenty of holes, to the point where it doesn’t really work from a logical standpoint. Oh well.
Common Knowledge
As another side note, I wanted to take a moment to address the prevailing theory regarding this. I am in fact fully aware of it, because it is so common as to have become basically the “de facto” theory that everyone spouts. That being, that Zero destroys all of the original series robots, and thus ushers in the X series.
No offense to anyone, but I never did buy this, personally, and it’s not canon. Recently Mr. Inafune over at Capcom indeed confirmed that this was never his plan for the series—he never viewed Zero as doing this either.
Still, I just wanted to mention this for the sake of completion, and so that people know they can stop mailing me about it now. 
Conclusions
So the end result is that we don’t really know who X actually is, as Capcom hasn’t said. Eventually they will probably have to do so in some way—though who knows, they may avoid the subject perpetually. But we won’t know for certain one way or another until they actually do it.
So for now, we know that X was created by a Dr. Thomas Light, but Capcom has never said what relation (if any) X has to Mega Man. Likewise, Zero was created by a Dr. Wily. But that’s about all that can be extracted from the games. The rest, for now, falls into the realm of fan fiction.
Postscript
On a complete side note, have you ever noticed that X and Zero have never taken their helmets off in Capcom’s games? Being Dr. Light’s creation, I assume X could take his helmet off (since Mega Man can), but I don’t really see why Dr. Wily would bother giving Zero hair and all of that considering Zero was probably built to be a war machine. But then, he gave him that ponytail attached to the back of his helmet which seems to serve no purpose, so maybe Wily is just plain eccentric.
I’ve never seen them take their armor off either (and put on clothes like Mega Man can do) in any of the games, but since X and Zero have no lives, I would not expect them to ever have to bother with things like clothing either.