Halo: Combat Evolved
You can see an unarmed Marine on Halo: Combat Evolved on 343 Guilty Spark if you accomplish the trick to board the Pelican that has just dropped you off. Simply grenade jump yourself to stay in the Pelican. You can travel over the map; then, on top of the building where you first meet the Flood Combat Form, there is a marine you can drop down to. He is unarmed, and does not use an animation that would suggest he is meant to hold a weapon. This is an easter egg.
There is also a similar glitch where the very last Marine in all Pelicans has no weapon, but their hands are in position of wielding an Assault rifle.
During the level Cairo Station, at the part where Johnson and Commander Miranda Keyes and two Marines are fighting off Covenant, you can actually take away a Marine's weapon. First, kill all the Covenant. Then, when a Marine fires his SMG at a body, swap weapons with him (it works best if you have a M6C Magnum). With luck, the Marine will not pick up the pistol and will run around without a weapon. It is possible to do this on other levels. Also, If you have an SMG as a secondary weapon and a pistol as a primary weapon, and trade the pistol for a marine's SMG, he will not receive the pistol and the marine will drop the SMG and be unarmed. This is rare and is best done on Cairo Station.
On the level Metropolis, it is possible to find a Marine without a gun. Fight your way through the level until you get to the area where Cortana says "There are some marines trapped in that building. Concentrate on the Wraiths...they're the biggest threat."
Keep fighting until the doors to the base open. Then carefully reverse park a Warthog or Ghost near the door. Head up the first flight of stairs, then halfway up the second, then head back down to the entrance. If done right, the Scarab should approach. Quickly jump into your vehicle and head to the Scorpion Tank. Get out and kick the driver out of the tank, saving the tank from destruction. If you look at the driver, he will have no gun. This Marine will not take any weapons you offer him. Also, if you get him inside a Warthog his body will float out of his seat; this is either because his death is scripted or the unarmed marine biped simply doesn't have the animation.
One more instance is on the level Regret, when the Marines get inside the elevator, trade your weapons with his. You will get his weapon but he will not get yours. He has to be on the inside of the elevator while you are on the outside.
The Great Journey
Commander Miranda Keyes in The Great Journey has no weapon, and will not take one, although she frequently crouches and holds her hands out as if she does.
It is also possible in Halo 3, sometimes on the level Sierra 117. However, it only works with Gunnery Sergeant Pete Stacker. It is only possible to do this with a Pistol and Spiker. Also, Floodgate, the Suicidal Marine may not actually have a magnum in his hands, but acts like he's pointing one.
This can also be accomplished on the Ark. First just play the level like normal, but carry a deployable cover with you until you reach the top of building with the Scarab. Go through kill all the Covenant, but it is important you keep the Marines alive (obviously) and they and you have dual-wieldable weapons (Plasma Pistols are preferred as it is unknown if it will work with any other dual weapon, this was found recently). Get the Marines in the hallway with the door leading to the Cartographer, deploy the cover in the doorway to prevent them from leaving (this will also protect them when the Covenant come). Activate the Cartographer, go back don't kill the Covenant, swap your dual weapons for a Marine's. He or she will then not take the weapon and you will get his or her gun. You can try this with the other Marine as well.