Unwinnable by Mistake/Tabletop Games

Warhammer 40,000

 * It is possible to win a game of Warhammer 40,000 by killing all of the enemy units that can claim objectives, making the game unwinnable for that side. Other units can still contest objectives, so a draw is still possible.
 * This was built into one of the armies, the Necrons, who used to just disappear if more than 75% of their army is utterly destroyed. Note that "army" in this case means the total number of units with the "necron" rule; there were a considerable number of units without this rule. This superseded all other official mission rules.
 * Close Combat with certain units. Due to the "you cannot wound creatures with a toughness that's 4 higher than your strength" rule and the "roll a D6 and add the result to your strength for Armour penetration" rule, it is very possible for you to run into combat with a dreadnought or a Wraithlord, only to realise there's absolutely nothing you can do other than wait till every single one of your models in that unit is curbstomped to hell. 5th edition got a little better where even the most basic units carry Krak grenades, which are strong enough to hurt Dreadnoughts (but still not Wraithlords). The Soul Grinder is even more dangerous, as it has an Armour rating of 13, meaning that unless you brought dedicated anti-armor close combat weapons against it, not even your grenades will help you (and in some cases, the weapon wont even help).
 * There is also an army-wide variant of this. Any wise opponent would bring at least some form of anti-armor against you, especially if they know you to use tanks. However, if you destroy all their heavy weapons, it's very possible to win by default (only in certain missions, however, like Annhilation). This is especially obvious with the new Imperial Guard Codex, where most of the MTBs have an armor rating of 11 on the back, meaning most people would be unable to even break those tanks in close combat, making the game very literally unwinnable.
 * Deepstriking units are not placed on the table and randomly come in during the game. However, if all your available troops are killed before the Deepstriking ones arrive, you automatically lose since you have no more units. This can be caused by a considerably bad roll, but is much more pronounced for Daemon Armies, where the entire army must deepstrike, which stands a very good chance that either all of them would get shot to hell in the first turn before the rest of your army comes (you can only shoot or run on the turn you deepstrike and only one type of unit in the army can actually shoot, meaning the entire army is slowed by at least a turn), or you scatter into other units and/or off the table, destroying what little troops you start with and fork over an automatic victory to your opponent.
 * If your opponent has some form of mobile unit and all you have is units with Rage, you can never win. Rage forces the unit afflicted with it to run towards the nearest enemy unit, which means if your nearest target is outside of your maximum move + run range (usually 12") then you won't get near enough to cause damage. Your opponent can then use his turn to move another mobile unit into Rage's area and move the other out of it, causing the unit to run straight towards the other one. In this way, your opponent can play "tennis" with your units while pumping gunshots into them, claiming objectives round the board and generally screwing around with no risk of any injury. And to make matters worse, the units acting as the "rackets" are usually vehicles, meaning that unless you somehow get in range to assault them you will be unable to damage them because Rage forces you to move, forbidding the use of heavy weapons.
 * A hilarious one can happen if you decide to hold your entire army in reserve and there are no deployment restrictions (only possible in certain gametypes): Your opponent can deploy his entire army near-touching your board edge (infiltrators can deploy even there, without any units to keep them at bay) and your units can no longer legally come on. This is because they must legally move the entire unit onto the battlefield without getting within 1 inch of an enemy unit or breaking through their formations, which you can no longer do. This actually happened — search for "Kroot Conga Line".

Dungeons & Dragons

 * Dungeons & Dragons adventure I5 Lost Tomb of Martek. The three Star Gems must be placed in the altar in the Garden of the Cursed so the PCs can continue. However, the Star Gems are also needed much later in the adventure to revive Martek, but there's no way for the PCs to know this. If they assume the Star Gems have fulfilled their purpose and forget to remove them from the altar, they're in trouble. The Crystal Prism area effect that teleports the PCs to the Citadel of Martek only works once. Once they reach the Citadel, even if they use the Teleport wall in the Citadel to return to the Garden of the Cursed to get the Star Gems they can't get to the Citadel of Martek again.