Very very confusing and deep... Read every word carefully and understand it before you go catch The Matrix Revolutions.

Unfortunately, "The One" program must be re-used each time, or
copied, so it can be "attached" to a new anomaly inside the Matrix.
So what happens to the old "The One" program? It faces deletion,
and as the Oracle explained, it goes into exile instead, just like
the French bloke (the Merovingian) did. He was the first One
(probably from the second version of the Matrix), and once he
fulfilled his duty, he became an exile program and "abdicated" his
"Oneness" by choosing Persephone and power. This is evident in the
bogs when Persephone asks Neo to kiss her. She says she wants him
to kiss her so she can feel what it is like again to be kissed by
something close to human, just like the Merovingian used to be.
Then she says to Trinity that she envies her, but that these things
are not meant to last. So the Merovingian used to be just like Neo
- a One - thus proving further the feedback-loop explained earlier.

The correct door in the Architect's room
Now there are two possibilities here:

1. All the previous One's chose the right door allowing a
"temporary dissemination" of their code into the Matrix (i.e., the
code they "carry" thus indicating Neo is indeed human), then he
must select (unplug) 23 people from the Matrix to rebuild Zion. This takes away the
possibility that stories from previous rebuilds of Zion will be carried
through. But Morpheus indicated in the first Matrix that this is the
case anyway. He said, "there was a man born inside, able to change
things, it was he who freed the first of us," - basically the One
previous to Neo. And this proves that the previous One chose the right
door also. Neo's purpose is also to choose the right door, but he does
not because he faces deletion afterwards and has the choice of going
into exile - programs choosing to go into exile is the one thing that
can't be accounted for in program parameters. Thus, he chooses the left
door instead this time. How was Neo able to choose the other door?
Because of his extreme willpower? - Even the Architect indicated that
he'd noticed this - "Interesting. That was quicker than the others." Or
more likely, because the Oracle upgraded his coding with the candy on
the park bench. The candy/cookie was a method to change the One's
program. She said he has made a believer out of her - this is quite
human-like and perhaps the previous One's didn't accept the upgrade
candy, now she has hope... hope that Neo will finally choose the other
door.

2. All the previous One's chose the left door, saving Trinity and
letting Zion fall. So this time is no different. But the Architect
does say, "You are here because Zion is about to be destroyed. Its
every living inhabitant terminated, its entire existence
eradicated," and also, "this will be the sixth time we have
destroyed it, and we have become exceedingly efficient at it," -
assuming the Architect isn't lying, then they have already
destroyed Zion (i.e., Zion has fallen) five times - i.e., the
result of going through the left door.

Morpheus and Trinity are programs.
Morpheus's purpose was to find the One and deliver him to the
Architect. Trinity's purpose is to control the One by getting in
love with him. Trinity is supposed to be the mother of the new One
every time the Matrix is Reloaded. That's why the sex scene was so
important and why she was named Trinity.

The Architect says, "she is going to die, and there is nothing that
you can do to stop it." He was correct though because she did die
just like Neo did in the first Matrix (Oracle said he or Morpheus
would, and she didn't lie, but he came back to life). Trinity dies,
but comes back to life (we are using medical definition of death in
all this of course!).

The Architect has already laid down an ultimatum for Neo choosing
the left door:

The Architect - "Failure to comply with this process will result in
a cataclysmic system crash killing everyone connected to the
matrix, which coupled with the extermination of Zion will
ultimately result in the extinction of the entire human race."

Neo - "You won't let it happen, you can't. You need human beings to
survive."

The Architect - "There are levels of survival we are prepared to
accept. However, the relevant issue is whether or not you are ready
to accept the responsibility for the death of every human being in
this world."

Looking at this further, the Architect does say "coupled" with the
extermination of Zion will the human race be exterminated. So he
says everyone connected to the Matrix will die, but if Zion is not
exterminated, the human race will not necessarily die. Also, there
is likely to be a time-window between not going through the right
door, and the cataclysmic crash, thus allowing Neo to unplug as
many as possible from the Matrix, then those people won't die. This
will be the start of the next Zion. As for the Matrix, a
cataclysmic crash doesn't mean the end of the Matrix - just needs
rebooting or reloading!

Agent Smith is the only "human" in this world. He's the one
spreading himself like a virus replicating himself over and over
until the Matrix will finally get overloaded and fail. Smith is the
one who wants to get out of the Matrix for good. He said so in the
first Matrix, "I must get out of here, I must get free! And in this
mind, is the key," squeezing Morpheus's temples, "my key! Once Zion
is destroyed, there is no need for me to be here!"Smith knows that
by killing Neo he can escape the Matrix because Neo is the key to
resetting the Matrix, or to shut it off. It was originally killing
Neo (in the first Matrix) that allowed Smith to become powerful
(cloning ability) - so killing Neo again will allow him to gain
Neo's powers completely, and thus gain the power to shut down the
Matrix.

So where the hell did Smith come from if he wants to destroy the
Matrix? He's obviously not meant to be there - he's a computer
virus as he has every characteristic of a virus - he multiplies and
spreads and infects (and emulates) other programs like one. He is
exactly as he described humans at the end of the first Matrix -
"You move to an area and you multiply and multiply until every
natural resource is consumed and the only way you can survive is to
spread to another area. There is another organism on this planet
that follows the same pattern. Do you know what it is? A virus."
But who put him there? This will only be revealed in
Revolutions(Revelations?) I guess - but I'm betting on humans in
the real real world, i.e., outside of Zion and the Matrix. They're
at war with the machines and trying to destroy them by infecting
them with this virus - Agent Smith. So the irony with this theory
is that Agent Smith represents the human race!! Neo represents the
machines! Agent Smith says to Neo just after he's seen the Oracle
that he became free when Neo destroyed him in the first Matrix
(remember when Neo entered his body and exploded him from inside
out) - as a virus, Smith has the ability to "inherit" other
programs' abilities and thus inherited some of Neo's.

The anomaly is all the humans that do not accept the Matrix. The
Architect says "Your life is the sum of a remainder of an
unbalanced equation inherent to the programming of the matrix. You
are the eventuality of an anomaly, which despite my sincerest
efforts I have been unable to eliminate from what is otherwise a
harmony of mathematical precision. While it remains a burden to
sedulously avoid it, it is not unexpected, and thus not beyond a
measure of control." This includes Neo, but Neo's Matrix avatar is
attached with the One program so that he can follow his purpose as
explained earlier under "The One explained".

However, he is also supposed to protect himself and destroy
anything that gets in his way - i.e., Agent Smith - so that he may
fulfil his purpose. Further proving Neo - and other non-accepters
of the Matrix - are the anomaly, the Architect says, "Your life is
the sum of a remainder of an unbalanced equation inherent to the
programming of the matrix." The clue here is Neo's program name -
"The One". Take one- third for example. 1 over 3 is 0.33333
recurring. A computer cannot deal with recurring numbers, so must
accept a limit, let's say 0.33333 for argument's sake. Multiply by
3, you get 0.99999 - never 1.00000, where has the "remainder"
0.00001 (One) gone? This is the limitation of computers, this is
the mathematical imprecision inherent in programming (of the
Matrix) and the eventuality of the One anomaly unable to be
eliminated.

What is the equation then?
Not sure, but it definitely involves pi. The Keymaker refers to the
window of time to open the door to the mainframe as 314 seconds.
3.14 is pi to three sig. figs., or the number of radians in half a
circle. Half a circle is like the cross-section of a womb, similar
to the alcove of Neo and Trinity's love scene - conceiving the next
One? "NEO", incidently, is an anagram of "ONE". Trinity and Neo -
one on one; a choice - one or one. Leads us to 101. "101" is
mentioned numerous times in Matrix 1 and Reloaded. Neo's room at
the beginning, Merovingian is on the 101st floor, the 101 freeway
of the car chase in Reloaded, then when Trinity is hacking into the
power plant system, she resets the password to Z10N0101. Freaky.
Indicates that she is a program because that's not some random
password she's put in. 101 is binary for 5, which in zero-based
binary counting: 000 is 1, 001, is 2, 010 is 3, 011 is 4, 100 is 5,
101 is 6 - And this is the 6th version of the Matrix! Then there's
303. 303 is the room Neo got shot in Matrix 1, the Oracle lives in
room 303, it's also the hotel room number Trinity is in in Matrix 1
and it's seen at the end when Neo fights the Agents and Smith and
begins to literally see the code that makes up the Matrix. 101 x 3
= 303, a trilogy, 3 + 0 + 3 = 6 = the 6th Matrix. Trinity means 3.

Who is the "mother" that the Architect refers to?
The Architect says, "Please," in an almost disapproving sense when
Neo suggests the Oracle, but does not reveal who it really is or
even directly that Neo is wrong. The architect was the one who
created the Matrix; the co-creator is neither Persephone nor the
Oracle. Both of them are only programs that have a purpose in the
matrix, just like the rest. The Architect is in charge of the
Matrix world and the co-creator is in charge of Zion. She has
almost the same age as the Architect. Therefore, that woman is the
Head Counsellor, the only woman of importance that lives in Zion
and the one who asked for the two captains to volunteer at the
council meeting. She's the one who knew all along about the Matrix.
She was the one who told Zion's Defence Minister to cool off and to
let Morpheus do his work so things could go as planned. Or
alternatively, it could indeed be the Oracle. She is the only
program that truly wants humans to have a free choice... at the
same time, she sees the future, because she knows the program code
- she is like God - which is why Seraph protects her - see "Who is
Seraph?" below.

What's so special about Neo's avatar?
Neo is a skilled hacker, and his avatar in the Matrix is based on
the person that founded the AI of the original machines that
eventually took over the world... How? Take a look at the disc he
gave to the bloke at the door at the beginning of Matrix 1. It said
"DISC AI" on it. The hollowed book Neo takes the disc out of is
"Simulacra and Simulation" - a collection of essays by the French
postmodernist philosopher Jean Baudrillard. He opens it to the
section "on Nihilism" (meaning nothing is truly known, etc.).
"Baudrillard's concept of simulation is the creation of the real
through conceptual or 'mythological' models which have no
connection or origin in reality. The model becomes the determinant
of our perception of reality--the real." And Morpheus says,
"Welcome to the desert of the real," in Matrix 1. I'd say this book
describes The Matrix to a tee. So this disc contains the key to the
AI, and thus how to destroy the machines, so I think they'll use
this info in Revolutions to ultimately destroy the machines, which
means he'll have to go back to the nightclub and find the guy he
gave it to.

The Twins
They are exiled programs that emulate the human myth of ghosts as
the Oracle explained. They are programs behaving badly. Persephone
killed one of the Merovingian's bodyguards with a silver bullet
because he was emulating a werewolf. So if the Twins could phase
into ghost form, why didn't he when his arm was trapped in the door
of the garage? Was it because he was wounded or because he can't
phase when his arm is trapped? No of course not. The doors of that
building, when shut, always led somewhere else (usually in the
mountains) when opened again without the Keymaker's key. So if it
were slammed shut due to the Twin phasing into ghost form, the
Twin's arm would've ended up god knows where, but certainly not
attached to the Twin's body.