The Living Dead

This has nothing to do with The Undead. We hope.

There are two ways to simulate corpses on TV -- get a good dummy or model, or use a live actor.

The problem with using a live actor is that they're a live actor. Live actors need to breathe. Either they hold their breath, the camera doesn't let you see their chest, or you get The Living Dead -- when you see a corpse visibly breathe on camera.

Modern special effects have introduced another option, of course; for that reason, this trope rarely appears in more recent movies (big-budget ones, anyway), which tend to have larger budgets and therefore can afford the special effects and editing to ensure that dead actors appear properly dead.

Literature

 * Two cases in Dalziel and Pascoe -- one involving a woman who had been dead for over a decade (she'd been embalmed).

Live-Action TV

 * In the premiere episode of Climax, an anthology of dramatic adaptations performed live, the corpse actually got up and walked away, unaware that the cameras were rolling. See this Snopes link.
 * On TV's Bloopers and Practical Jokes, a prank involving a visit to a funeral home was foiled when the casketed corpse at the center of the joke couldn't hide his breathing.
 * The fact that a prepared corpse in a funeral home looks nothing like a live person was evidently lost on the proprietors of that joke.
 * Not breathing, but equally revealing; in the Doctor Who episode 'The Unquiet Dead', a character opens a coffin and the corpse's eyes twitch noticably. To be fair though, that episode was about dead bodies getting up and walking around.
 * One outtake of The X-Files had Scully declaring that a man was dead...just as he sneezed loudly. She continues to deadpan, "He's dead Mulder. He's dead and he's not coming back," as the rest of the production crew cracks up.
 * Dutch Long Runner Baanttjer had this and actual Dutch celebs would feature as stiff of the week.