Halo 2: on Legendary, if one person dies it resets you to the checkpoint.
Halo 1/3/Reach: If one person dies they wait to respawn until (one of) the still-living person (people) can get to safety. If (all) the still-living person (people) die(s) before that happens, it resets to the checkpoint.
Halo 3/Reach: If you turn Iron Skull on, if one person dies it resets you to the checkpoint, if everyone dies at the same time it resets you to the beginning of the level.