Rex

The word Rex can be found in Halo: Combat Evolved, Halo 2, and Halo 3. Bungie programmer Tyson Green (username Ferrex) planted an Easter egg in Halo: Combat Evolved and Halo 2.

The Maw
The word "Rex" can be found in the level The Maw, written on a wall in blood.

Directions

 * 1) Proceed normally through The Maw on any difficulty level, until you get to the huge Warthog jump/free fall.
 * 2) At the ledge, drive the Warthog to the right, so you land on the side of the floating platform.
 * 3) Enter the corridor and look to the right side, spelled out in blood is the word Rex, on the other side is a bloody swastika.

Outskirts
On Outskirts, the word Rex is spelled in rocks with a pool of blood and a Covenant Energy Sword is sticking out of the ground.

Directions

 * 1) Get to the the rooftops and go to the area where the Jackal Snipers and Drones are.
 * 2) Keep going until you reach the building with two snipers in it.
 * 3) Turn and there should be a room in a building you can jump into, the Rex is in there, along with the sword. Keep in mind though that the Rex is not always in there and when it's not, the sword may not have infinite energy. Also, Rex does not appear in co-operative games.

Great Journey Rex
On top of the final tower in the Great Journey, there is a bloody REX written in Flood blood.

Directions
It seems that the only way to see this particular Rex is by using Dev Cam mode, unless you have a plasma grenade pile and a Ghost with the Sputnik Skull turned on. A video of how to get it is here. 

Cortana Rex
In one of the larger rooms in the level, on top of one of the ledges, you will see "Rex" etched into the wall.

Directions
In between points T and U (see level map in official guide), when you come into a large room, you will see a ledge to your right, go up and turn to your right and you will find Rex scratched into the wall.