A phenomenon in video games where the player loses a life without warning.
The earliest examples of sudden death can be found in certain text adventures. For example, if I chose to go north only to be informed that I had fallen into a pit of spikes and died, that would a sudden death and considered grossly unfair - assuming there was absolutely no hint or warning available. In the 8 bit days or time-consuming tape saves (if any), the sudden death was an infuriating setback. In adventure games, the textbook sudden death would present you with a description of your demise and the cherished phrase "YOU ARE DEAD".
Another breeding ground for sudden deaths is the 3D platformer or FPS. When you walk into an unmarked trap, that's a sudden death. When the signs of danger - a subtly different texture on a wooden floor, for example - are not demonstrated in advance (e.g. by the death of a NPC, or a note of caution in the mission notes), that is also a sudden death. If you're presented with three identical buttons and pressing one of them will make you explode, you'd better believe that's a sudden death. The worst manifestation of sudden death is the game that forces you to navigate a level through trial and error, by "learning" where not to go and what not to do over the course of several deaths.
Certain game types lend themselves to sudden death more than others; it would be impossible to encounter a sudden death in Pac-Man or Tetris. It's worth pointing out that games of this ilk are often converted from or to coin-op versions, and it's unlikely a title that threatened sudden death would attract paying customers for very long. As a result, console or PC games involving exploration of hazardous environments are the most vulnerable genre.
(It is possible to suffer a kind of sudden death in Asteroids, but that's the calculated risk that limits the power of the hyperspace button, and as such is a valid design element - you must choose to expose yourself to the risk.)
The development of fast storage for saved games (the PC's quick save facility in particular) makes the sudden death less of a burden today than it used to be, but at the same time there's an argument to be made that quick saves and the like have made the sudden death a convenient device for the lazy designer who needs to pad out a level or two. At any rate, the phenomenon remains a demonstration of poor design that should never make it past QA.