3e has
Do you cheat? The answer: The DM really can’t cheat. You’re the umpire, and what you say goes. As such, it’s certainly within your rights to sway things one way or another to keep people happy or keep things running smoothly. It’s no fun losing a long term character who gets run over by a cart. A good rule of thumb is that a character shouldn’t die in a trivial way because of some fluke of the dice unless he or she was doing something really stupid at the time.
4e has
Rolling behind the screen lets you fudge if you want to. If two critical hits in a row would kill a character, you might want to change the second critical hit to a normal hit, or even a miss. Don’t do it too often, though, and don’t let on that you’re doing it, or the other players feel as though they don’t face any real risk—or worse, that you’re playing favorites.
AD&D has
Now and then a player will die through no fault of his own. He or she will have done everything correctly, taken every reasonable precaution, but still the freakish roll of the dice will kill the character. In the long run you should let such things pass as the players will kill more than one opponent with their own freakish rolls at some later time. Yet you do have the right to arbitrate the situation. You can rule that the player, instead of dying, is knocked unconscious, loses a limb, is blinded in one eye or invoke any reasonably severe penalty that still takes into account what the monster has done. It is very demoralizing to the players to lose a cared-for-player character when they have played well. When they have done something stupid or have not taken precautions, then let the dice fall where they may!
Expert (Mentzer) has
The DM may choose a number within the given die range rather than roll for the amount of damage, number appearing, etc. This may be necessary to allow for a more enjoyable game; heavy damage early in the game may spoil some of the fun.