Rex

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

Maw Rex
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/freefall.
 * 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 Rex
On Outskirts in Halo 2 the word Rex spelled in rocks with a pool of blood and Covenant Energy Sword sticking out of the ground with infinite energy.

Directions

 * 1) Get on top of the roof tops 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.
 * 4) *EDIT*
 * 5) The Rex sword does not have infinite energy unless you use the infinite energy glitch and carry it over to Metro

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. Or a grenade pile and Ghost with the Sputnik skull on.