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.

Not to be confused with Corpsing, which is a different movie error with the same cause (the actor is doing something he shouldn't).

Examples of The Living Dead include:

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 & 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.