In the Anime
During the first series The Nightmare Begins, the first guest is led by Angel Dog/Devil Dog into the graveyard outside Gregory House in an "escape". He hides from Gregory who gives up searching when he says that the guest will come back inside. The first guest is met by Dead Body who offers him a drink. He shares the goal of escaping but notes that he can't due to his body's weakness to water and air. Dead Body tells the first guest that he needs a new body to escape. And he decides to take the first guest's body.
Dead Body chases the first guest through the graveyard until the guest reaches the doors. He slams them shut as Dead Body angrily demands that the first guest give him his body. Gregory welcomes the first guest back.
Dead Body was actually pretty civil and hospitable with the first guest before the attempted bodysnatching. Then, he became a hostile, angry force determined to get the first guest's body to use for an escape. He was also a drunk, mentioning that he spent his time prior to the first guest's appearance drinking his cares away.
Other Dead Bodies
In The Guest From Hell, Several Dead Bodies are seen booing Poor Conductor and tossing objects at him.
Two Dead Bodies appear during the third series The Last Train where they, like the one from The Nightmare Begins, desire to escape in new bodies. A drunken Gregory encourages them to drink with him and to follow that goal. The more determined Dead Body opens a window and this action results in one of the Dead Bodies being shattered by the wind while the other flees in terror, to meet the same fate afterwards. Gregory chuckles at this, noting that their "friendship was over."
Another Dead Body appears in the fourth and final series The Bloody Karte as a one-time patient of Catherine. Disappointed that he is a patient sans blood (he was actually in the hospital to get a blood transfusion), Catherine opens a window and lets the wind destroy the panicking Dead Body.