Invincible Marines can be seen in one level of Halo: Combat Evolved and on two levels on Halo 2.
Halo: Combat Evolved level
The Pillar of Autumn
The Halo: Combat Evolved Invincible Marines can be seen on the level The Pillar of Autumn. When Captain Jacob Keyes or any crewmember on the bridge is shot by the Master Chief, a group of invincible Marines come in and kill the Master Chief. This is not actually a glitch, though, but a programmed action for shooting the captain.
Halo 2 levels
Outskirts
On the level Outskirts, advance to the part where you ore offered the Warthog after getting the hidden sword. The marines inside will get in the gunner and passenger seat. Advance to the part where the chapter title is "A Day At the Beach". If you get out of the Warthog and shoot or melee them with an energy sword, sniper rifle to the head, or any weapon, they will not die. These Marines might be useful when you have to go through the tunnel.
Metropolis
On the level Metropolis play through till you get to the part with the two Marines in the Warthog at the tunnel. Destroy the Warthog before you get to the wall area with Jackals. The Marines will be alive, the Warthog done for, and your two Invincible Marines still alive with their invincibility intact.