Mann Vs. Machine is a game mode in the works, which will somehow involve a team of AI controlled robots. Not much is known about the actual gameplay of MvM yet.
The MvM legacy started back in May of 2010, when the Engineer Update Teaser trailer was released.
In the foreground of the trailer, at around 9 seconds, we see a robot head, like this one. on the table, and at 15 seconds, we can see another robot head in the bottom-right. w Then, on July 5th, 2010, The Engineer update page on the TF2 Blog went live. On this page, there is an image of a Scout robot, in a parody of Da Vinci's 'Vitruvian man'.
Jump forward to December 15, 2011, and the release of cp_foundry. There are two secret rooms on foundry, that can only be reached using No-clip, One behind RED's spawn room, and one near BLU's second point. The first hidden room is behind a door labelled "TOP SECRET", guarded by a RED soldier. Inside, there is a RED Heavy, and RED Scout, looking at four photos on a line.. Also, written on the wall of the secret room are the numbers "1961 13 22 13". 1961 is the year that the first Production Line robot was put to work. If we give each letter of the Alphabet a numerical value (A = 1, B = 2 etc.), then "13 22 13" becomes "MVM".
The second secret room resembles a disused garage, but on the wall, there is an advertisement for "Doctor Wilson's Auto-Borax self scrubbing mechanical soap". Two planks placed in front of the advertisement highlight the letters "TO-BOR". 'TOBOR' is 'ROBOT' backwards.
Jump forward once again, to the Fifth of May this year, and these files are added to the game in a patch.
The June 19, 2012 patch adds the 'Mysterious Treasures' in the lead up to the Pyromania update, including the "Damaged Capacitor", which, along with the "Secret Diary" survives the Pyromania update, and is not reduced to Ashes, like the other items. The Damaged Capacitor may be somehow linked to MvM, since it is an electrical part. There are also a series of 6 numbers on the Capacitor: "07 18 01 25". Using the same code as earlier, this spells "GRAY".
At the end of the Pyromania update, and with the release of Meet the Pyro, Valve releases the Source Film Maker Beta. The SFM beta contains models of robot heads for each of the 9 classes.
Also, the Pyromania update added sd_doomsday, which contains another secret room behind BLU's spawn room. The room is guarded by a BLU soldier, and contains the same 4 photos from the cp_foundry secret room and a BLU Spy, looking at a map, which appears to depict three maps.
Fast forward one more time to the 9th of August, and the appearance of a blood splatter on www.teamfortress.com, on the "FREE TO PLAY" banner at the head of the page. Clicking the blood splatter leads to this image, which appears to be a Birth certificate for the Three Mann Brothers, Redmond, Blutarch and Gray. (Credit to wickedplayer494 for finding this)
It is speculated, that there will be a third team, GRAY team, which was founded by Gray Mann (Who may be in possession of Radigan Conagher's 3rd Life Extender machine) consisting entirely of Robots, based on the 9 mercenaries from RED and BLU team.
In the Birth certificate, it says that Gray "absconded to the Scourge of London, the EAGLE." It is speculated that this means he ran away and hid in the USA, which would point to Senator Gray/Grey in the Poopy Joe files.
Also on the 9th of August, a post on the Source Film Maker blog titled "I am a Robot" features an image of the RED soldier in his Robot Halloween costume.
If you feel that I've missed anything, or have made a mistake, please let me know, and I'll edit the post.
Hope this helps get you up to date!
--EDITS--
It's highly likely that the person ripped out of the Scream Fortress Mann Family Portrait is Gray Mann.
Buster_Gonad reminded me of this hidden page from teamfortress.com.
In The Last Will and Testament of Zepheniah Mann, it is believed that the obscured name could be 'Gray Mann'.
There are also some as yet unused "Bomb" animations in the files for the Soldier, which may relate to MvM.
Added the meaning of the numbers on the Capacitor - Thanks to HeimlichCounter.
Added the info about Gray being "absconded with by the EAGLE". - Thanks to Man-to-Sack.
As of the August 10th Patch, Carrier Tanks have been added to the sky boxes for 2fort, Granary, Badwater Basin and Doublecross.
Read hogofwar's comment below for info about the various MvM related files added to the game.
A new blood splatter on the TF2 blog leads to this clean image of Zepheniah Mann's will
As of the August 12 patch, the Barely Melted Capacitor can now be equipped in a misc slot, but so far it's only known effect, is that whenever someone wearing the capacitor high fives a player, a joke will be written in the chat window. Many examples of these jokes can be found here.
This comic was just released on teamfortress.com after someone managed to decode the "jokes" leading to this crafting recipe, which when crafted, triggered a game wide alert containing the URL of the comic.
--Edit2--
If you look at the Damaged Capacitor's picture, you can see numbers on it: 07180125. If you take them as 4 pairs (07 18 01 25) and treat them as letters of the alphabet (01=A .. 26=Z), that spells out GRAY.