The Call of Cthulhu games are known for being ruthlessly brutal - an antidote to the relative safety that the heroes enjoy in other game, notably Dungeons & Dragons, where they can expect to live out most adventures. A player in Cthulhu should always keep spare character sheets to hand, and never get too attached to his hapless adventurer.
A rules-light Lovecraftian game called Cthulhu Dark takes this Up to Eleven by suggesting you might instead just bring a stack of index cards or a sticky-note pad instead of character sheets, your characters are so disposable.
Dark Heresy, Rogue Trader, Deathwatch, Black Crusade, and Only War of the Warhammer 40K RPG series certainly qualify. With only a limited amount of Wounds per character in comparison to the damage weapons can inflict, characters quickly burn through their health in fights. Though the game attempts to alleviate the problem by granting Fate Points, which can be used to avoid certain death, these too tend to get used up quickly.
The Legend of the Five Rings RPG is notorious for its lethality, and with good reason: with a dice pool task resolution system that allows you to keep the highest dice rolled in the pool, and the fact that rolling a ten (the highst number on a d10, the die type used by the game) on a die allows it to re-rolled and added onto the previous total in addition to the ten previously rolled allows for rolls (and in particular damage rolls) to become very high, often causing even the toughest character to die in one or two hits.
Stars Without Number doesn't quite go that far, but it's still a very deadly game where first level characters need to be careful about not getting shot at because a standard firearm will very likely kill them. There are suggestions for making it a bit less brutal, such as implementing a "dead at -10 instead of 0HP" rule, but ultimately the recommendation of bringing along a spare character sheet or two is in the corebook for a reason.