Character interludes

Through the Halo 3 campaign, there are "Moments" when either Cortana or the Gravemind telepathically address the Master Chief. During these Moments, the player's movements will slow drastically, as will their ability to turn and face another direction. A screen effect will alter the display of the game.

During a "Cortana Moment," the screen turns blue, and Cortana's image flashes in and out of focus on the screen. Her voice will contain a slight echo and sometimes a deeply-pitched distortion effect, and her image will erratically "jump" around the screen. During a Cortana Moment there will also be a noise sounding vaguely similar to the noise heard if you place a seashell to your ear (the sound of the sea).

During a "Gravemind Moment," the player's view become murky green, and "tentacles" can be seen at the edge of the screen. The screen will shake in unison with the Gravemind's voice, shaking far more violently if Gravemind is screaming or yelling in anger at John-117.

The Cortana moments depict her descent into rampancy, while the Gravemind moments are used to convey the point of view of the Flood. Checkpoints are usually attained after these moments. The player is almost never in any danger of damage while the Moments occur, which is fortunate, as the player cannot move quickly. It is possible in co-op mode for one player to trigger the Moment while the other player is behind fighting enemies that the first one skipped.

In Halo: Evolutions, however, the explanation of the Cortana Moments has been provided. It had revealed that the Gravemind had successfully hijacked Cortana's system, allowing him to speak with her voice. This was part of his plan to persuade Cortana and John-117 that Cortana was descending into rampancy. It is, however, unknown how the Gravemind was able to connect to John-117 all the way from High Charity.

Transcripts

A Cortana interlude during Halo 3 campaign level Sierra 117.

Cortana, in a Cortana Moment.

Arrival

Cortana {Voice Only}: "They let me pick, did I ever tell you that? ...choose whichever Spartan I wanted."

Cortana {Voice Only}: "You know me. I did my research. Watched as you became the soldier we needed you to be."

Cortana {Voice Only}: "Like the others, you were strong and swift and brave. A natural leader."

Cortana {Voice Only}: "But you had something they didn't. Something no one saw..."

Cortana {Voice Only}: "...but me."

Cortana {Voice Only}: "Can you guess?"

Cortana {Voice Only}: "Luck."

Cortana {Voice Only}: "Was I wrong?"

(Cortana Moment): "Don't make a girl a promise...if you know you can't keep it."

These moments happen during a cinematic and Cortana's face is not seen except for the last one listed.

Sierra 117

(Cortana Moment): "Could you sacrifice me to complete your mission? Could you watch me die?" (repeated quote from Dr. Halsey)

This and the last Arrival Moment are the only times any NPC's notice them.

Crows Nest

(Cortana Moment): "You have been called upon to serve." (repeated quote from Dr Halsey)
(Cortana Moment): "You will be the protector of Earth and all her colonies." (repeated quote from Dr Halsey)
(Cortana Moment): "There will be a great deal of hardship on the road ahead." (repeated quote from Dr Halsey)
(Cortana Moment): "You will become the best we can make you." (repeated quote from Dr Halsey)
(Cortana Moment): "This place will become your home." (repeated quote from Dr Halsey)
(Cortana Moment {Voice Only}): "This place will become your tomb."

The Storm

(Cortana Moment): "I have defied gods and demons..."
(Cortana Moment): "I am your shield... I am your sword." (Presumably a reference to Dr. Halsey's quote of how the Shield worlds were the Forerunner's "shields" and the Halo Installations were their "swords")
Cortana {Voice Only}: "This is the way the world ends..." (This moment happens during a cinematic and Cortana's face very briefly seen just before the screen goes black.)

Floodgate

(Cortana Moment): "Chief. {background mumbling} I can't tell you everything...it's not safe. The Gravemind... it knows I'm in the system..." {background mumbling}
(Gravemind Moment): "Do not be afraid. I am peace... I am salvation."
(Gravemind Moment): "I am a timeless chorus. Join your voice with mine, and sing victory everlasting!"

The Covenant

(Cortana Moment): "It asked, and I answered. (Her tone turns bitter) For a moment of safety, I loosed damnation on the stars."
(Cortana Moment): "I'm a thief... but I keep what I steal."

Cortana

A Gravemind Moment in Halo 3.

(Gravemind Moment): "Child of my enemy, why have you come? I offer no forgiveness... for a father's sins passed to his son."
(Cortana Moment): (A strange mix of cries of agony and manic laughter.)
(Gravemind Moment): "Of course, you came for her... We exist together now. Two corpses in one grave." (repeated quote from Halo 2 level High Charity)
(Cortana Moment {Voice Only}): "A collection of lies; that's all I am! Stolen thoughts and memories!"
(Gravemind Moment): "And yet, perhaps a part of her remains?"
(Cortana Moment {Voice Only}): (Laughter, in response to the Gravemind.)
(Gravemind Moment): (angry) "Time has taught me patience! But basking in new freedom, I will know all that I possess!"
(Cortana Moment {Voice Only}): "May I speak with you, please?... What's your name? It's very nice to meet you! ...You like games? So do I." (repeated quote from Dr Halsey)
(Cortana Moment): "It was the coin's fault! I wanted to make you strong; keep you safe. I'm sorry, I can't." (reference to Dr Halsey; only available upon accessing the eighth Terminal)
(Cortana Moment {Voice Only}): I'm just my mother's shadow. Don't look at me, don't listen! I'm not what I used to be..."
(Cortana Moment): (panicking) "I have walked the edge of the abyss. I have seen your future. And I have learned!" (Repeated quote from the Cortana Letters)
(Gravemind Moment): (angry) "Submit! End her torment and my own!"
(Cortana Moment): (panicking) "There will be no more sadness, no more anger, no more envy!" (Referencing rampancy and quoting the Cortana Letters)
(Gravemind Moment): (angry) "You will show me what she hides, or I shall feast upon your bones!"
(Cortana Moment): (speaking in a flat, monotone voice as though brainwashed. Her image is green.) "This is UNSC AI Serial Number CTN0452-9. I am a monument to all your sins." (quoting the Gravemind in the latter sentence)
(Gravemind Moment): (roars) "At last, I see! Her secret is revealed!"

Halo

(Gravemind Moment {Voice Only}): (taunting, angry) "Did you think me defeated?!"

(Gravemind Moment {Voice Only}): (enraged) "I have beaten fleets of thousands! Consumed a galaxy of flesh and mind and bone!"

(Gravemind Moment): "Do I take life, or kill it? Who is victim... and who is foe?"

(Gravemind Moment {Voice Only}): (sadly, defeated) "Resignation is my virtue...like water I ebb and flow. Defeat is simply an addition of time to a sentence I never deserved, but you imposed."

Trivia

If you use the 3 Player Local Co Op glitch, during the Cortana Moments, the game will freeze because it was not meant for three-player split-screen campaign. Strangely, Gravemind Moments function normally.
The moments could be caused from the Chief's CNI, because Cortana would be linked to it, and the Gravemind would be able to control it by projecting Cortana's and Dr. Halsey's memories.
If you take a screenshot of a Moment from the Theater, it will appear completely black in the screenshot gallery, adding some mystery to the entire perception.
During any of these moments, you are completely immune to damage and will not be attacked even by nearby enemies, causing anyone who goes into a Cortana or Gravemind Moment to be potently invincible for the moments Cortana or Gravemind speaks.
Excluding Arrival (where it should still be noted there is a Cortana Moment before choosing your controls) there are seven levels where the Gravemind and Cortana Moments occur.
Excluding the moment in Arrival, there are twenty-eight moments in total—seven times four.
If a Moment occurs while you're driving a vehicle, it slows down as well. However, if you are a passenger, then the vehicle goes at normal speed.
Moments will not slow down a jump, a melee, or attacking with something such as the Gravity Hammer.
The "It was the coin's fault" Moment in the level Cortana is a reference to Dr. Halsey's examination of a six-year-old John before he was drafted into the Spartan II program. Halsey flipped a 21st century quarter, and John correctly identified the eagle side of the coin that was about to the hit the ground before it did. Halsey explained to then-Commander Jacob Keyes that this was a means of weeding out the "unlucky" applicants, as there were only a limited number of slots available.
During the level The Covenant, as you enter the Control Room during the Cortana moment, if you look at the screens that, during the next cutscene, show the Prophet of Truth, you'll find that Cortana also shows up on them.
In one of the last Cortana Moments, Cortana turns green. In Halo: Combat Evolved, upon entering the computer systems of Installation 04's Control Room and being exposed to the wealth of information contained there, Cortana also turns green and begins to behave quite oddly, experiencing sharp mood swings and displaying rude contempt for both the Master Chief and 343 Guilty Spark. It is noted in Halo: First Strike that exposure to such floods of raw information can great shorten the operational lifespan of a smart AI. The presence of green, therefore, serves as an indication of rampancy (a reference to Marathon: Durandal).
In the level Cortana, there is a secret Terminal in the room where she says, "So you like games? So do I.". When the terminal is accessed, Cortana will completely take over John's HUD (as well as those of any other players, including Elites), mentioning the coin quote.
Many of Cortana's lines, as noted above, are repeated lines Dr. Halsey has said before. One such line is, "You will be the protector of Earth and all her colonies.", which Dr. Halsey says to the six-year-old Spartans in Halo: The Fall Of Reach. Cortana also recites a few lines from the Cortana Letters and Halo 3 Announcement Trailer.
In Sierra 117, the medic tells us that during the Cortana and Gravemind Moments, the player's vital signs momentarily ping KIA, which may be the reason you slow down, as the armor functions using the user's neural signs instead of muscles, which makes it still possible for the Master Chief to move even if his vital signs have stopped but his brain is intact and functioning.
During some of the moments, Gravemind dialogue from Halo 2 is re-used. In a Gravemind Moment, he repeats a line from the Halo 2 level High Charity when he broadcasts himself over High Charity's system in response to Truth, saying: "...we exist together now, two corpses in one grave." Another recycled line is from the cut scene during which the Gravemind introduces himself saying: "I? I am a monument to all of your sins." It is actually Cortana who repeats this line, displaying the extent of her corruption.
The messages: "I have defied gods and demons" and "I am your shield. I am your sword". The first line could refer to Cortana defying the will of the Forerunners (activating the Halos) and the will of the Flood (assimilating all life in the galaxy).
After any Cortana/Gravemind moments, there will be vertical lines running down Master Chief's HUD (or visor). The armor's helmet automatically refreshes the visor.
If there is background music playing during the gameplay, it will pause during any Cortana/Gravemind moments.
In the level The Covenant, if you force a Warthog into the Prophet's Citadel (using the Wraith) and drive straight for the door, nonstop, you may activate both the Cortana Moment and the preceding cutscene at the same time. During this, the cutscene will have a bluish tint with two extra blue layers. This effect could be what causes screenshots during Cortana Moments to blank out. Although it could also have been a desired side effect of Bungie to prevent all but cutscene screenshots of Cortana from being taken.
The fact that the Cortana Moments affect the Arbiter is quite odd, as the Arbiter has no connection to Cortana, and has no CNI that would allow her to communicate to him, as Captain Keyes did to the Chief. Bungie may have overlooked this problem, or intentionally left it so it wouldn't be that only one player would get the Cortana Moments. More than likely it is simply a gameplay aspect, and the Arbiter was not canonically privvy to the Moments.
Halo Evolutions shows the truth of some of this, though not how the Chief keeps experiencing these moments. Cortana battled the Gravemind, trying to hold onto the data about the Portal and the Ark (presumably gotten when she was in Alpha Halo's Control Center). She ends up creating multiple copies of herself to distract the Gravemind and twice they apparently chimed in during her conversations with the Gravemind. One added the "I am a monument to all your sins" part of one of the moments while the rest was Cortana defying Gravemind to buy the Master Chief some time. Cortana placed the message onto the ship by composing it with the help of a copy and then transmitting it to that ship through Gravemind's link to it, with part of it being coded to seek out and upload itself to the nearest data device. Gravemind knew and helped out as he wanted to lure all of his enemies to one place, but had no idea what the message actually said.

Gallery

A Cortana Moment.
Another Cortana Moment.
A Cortana Moment where she appears as green, a homage to Marathon: Durandal in which rampant AI appear green.
A Gravemind Moment in Halo 3.