(this is the translation of a French post I wrote in November 2004)
This is just a personal interpretation. There are others, and it's probably nothing other people didn't think about. For example, Matrix Happening explains the narration more than it tries to give a theory about the meaning of the events in the trilogy but it's a very good read if you understand French.
One thing that should have cought the attention of everyone and hint them that the real story wasn't as simple as the Wachowski would have you believe was the moment in Reloaded when Neo fights a sentinel in the "real world" with only the power of his mind. From this moment on, it becomes inconsistent to believe that the "real world" is just the future of our own. Neo's powers are supposed to come from his mastering the inner workings of the Matrix. How then could he have the same powers in the "real world" except if that world is itself a super-matrix? This is very explicitly confirmed later by the Architect, as well as by the infiltration of the real world by agent Smith (an agent in computers is of course an independant program that is devoted to a specific task and can sometimes propagate like a virus, and if Smith is a virus, Neo is the anti-virus in both worlds). One could also notice that this world is not called "real world" any more, but is now the "machine world". Neo sees the real nature of this world in the third episode under a form that looks very much like the Matrix itself and its trademark Kanji character rain (which was actually one of the things the Wachowskis took from Ghost in the Shell). Only the color changes from the green we've been used to to a flaming yellow that evokes hell. Finally, entities that are clearly defined as programs are now able to go from one world to the other through a train station.
Another clue is the Oracle's ability to foresee the actions of supposedly human beings. In the Matrix, only the machines should behave in a predictible fashion. It should thus be clear from the first episode that Neo is not human. The Architect confirms it in the second episode, Neo is just a program whose function he defined.
I don't hesitate to go further and conclude that there is not a single human being in all three movies, but only programs: all characters have names that indicate more function than personnality (Mouse, Link, Lock, Cypher, Oracle, Architect are all names that have a clear meaning in the computer world).
The keys to understanding Neo's name are given by the Oracle and the Architect. In the first movie, the Oracle tells Neo that he is not "the One". In the second movie, the Architect tells him that he is actually the sixth one to fulfill that function. All you have to do with this information is notice that One and Neo share the same three letters and count the different ways in which you can order three letters and you'll understand exactly what the Oracle and the Architect meant. One was just the first one, not some sort of messiah. Neo is the last one. Between them, the others were Oen, Eon, Eno and Noe. Furthermore, Neo means "new", which is its ultimate function for the Oracle. His previous name was Anderson, which means "the son of the man".
I think the human race has been wiped out during the war and only machines and programs remain. Some fulfill their tasks while perfectly knowing their nature while others believe they're human. The Architect's function is to make the Matrix last, to stabilize it, for example by deporting the perturbing elements to Zion.
The Oracle, according to its name, is the Matrix's database (I guess Sql Server would have been too obvious ;), but her goal seems to create something she can't predict (Neo and the little girl in the third episode?). In other words she's trying to recreate the human nature. Maybe that's what the Matrix was built for, and once again this is confirmed by the name of the Matrix and some troubling images such as spermatozoid-like sentinels penetrating Zion using giant drills...
The Wachowski brothers have been very litteral about almost everything but what's in plain view is often the most difficult to see.