MONOPOLY: The bank will never loan you any money, no matter how much real estate you own (you may mortgage properties, though).
In CANDY LAND, no one ever eats anything.
In MARVEL HEROCLIX, Captain America cannot break an ordinary store window.
In WARCRAFT II for the PC, a farm house, once burning, will keep burning for the rest of the game, without ever burning down. It will continue to produce resources while it does so.
In the PC game DIABLO, if you are not strong enough to wear Chain Mail Armor, you can carry it around in your backpack until you are strong enough to put it on.
In the PC game DIABLO, it is impossible to jump over a waist-high stone wall.
In the detective game CLUE, the murderer is not aware that he did it, and can win the game by catching himself.
In first-edition ADVANCED DUNGEONS AND DRAGONS, a 12th-level fighter, statistically, could survive a fall from pretty much any height (based on average hit points for a 12th level fighter vs. the average falling damage from any given height).
In MAGIC: THE GATHERING, demons can benefit from Blessing and Holy Strength spells.
In the MUNCHKIN card game, it is possible for one player to be half elf, half dwarf, and half human.
In the aircraft miniatures game CRIMSON SKIES, five planes cannot fly the same maneuver in formation. In fact, unless you’re playing the Hollywood Knights squadron, no more than TWO planes can fly the same maneuver simultaneously (although this only goes for the most recent version of the game).
The PC game SYSTEM SHOCK II takes place in a high-tech future where space travel and laser pistols are possible… but an ordinary pistol, brand new, cannot fire more than fifty bullets or so without breaking.
In the NUCLEAR WAR card game, it is possible for one country to completely depopulate another country by subjecting them to propaganda. (The entire population picks up and moves!)
In the role-playing game CALL OF CTHULHU, players’ characters routinely go insane. Under many circumstances, players may continue to play their crazy characters.
In the PC game THEME HOSPITAL, if you forget to put bathrooms in your hospital, patients will crap in the middle of the halls.
In the PC game, THE SIMS, sims can never have sex. In order to allow sex, players must purchase the LIVIN’ LARGE expansion.
Can anyone add to the list?