Roguelikes. Their defining feature is having one life which, when lost, also deletes your save. Combining this with (seemingly) Everything Trying to Kill You and (often) dying repeatedly whilst learning how to survive in the gameworld ("Medusa - causes petrification. Sadly, so does eating her corpse") is part of the attraction.
Part of the difficulty in NetHack is caused by the sheer randomness of the game with limited efforts to balance. There was one player who died without ever taking a turn - all because the game generated a random monster in line of sight of them at the start of the game, then randomly generated a wand in the possession of the monster, and randomly selected that wand to be a wand of death.
Slash EM is another variant that takes NetHack and ups the ante. "NetHack doesn't care if you live or die. Slash'EM wants you dead."
Is NetHack too easy for you? Then it's time to play ADOM. Yup, it's a roguelike with a world map. Which means that there are multiple randomly-generated death trap dungeons for you to perish in. It's not uncommon for gamers to play a month or two before even getting to the main dungeon. And unlike NetHack, it only gets harder as you play. (If it takes a year before the average first win in 'NetHack, it takes about 5 years for ADOM''. And let's not even mention the ultra endings...)
The worst Roguelike of all is probably Iter Vehemens Ad Necem (usually called IVAN). Its name translates from Latin as "A Violent Road To Death." It's intended to be effectively Unwinnable, although some players have managed to win anyway. This is a bug and will be fixed in the next release.
Dwarf Fortress, where the main question is not "will your fortress collapse?" but "when and how will your fortress collapse?"
This is turned Up to Eleven by the "Dig Deeper" mod, which introduces orcs: trap-proof, door-unlocking fiends that turn up in huge numbers before the end of the first in-game year. (It's possible to end up outnumbered 7:1 by Orc mobs appearing before you've even got your first immigration wave, complete with Orc spearmasters, archers and mace lords).
The postgame of each Pokémon Mystery Dungeon game. After you finish the story mode, some of the BonusDungeons that you can unlock are sadistic. Examples include: Western Cave and Silver Trench in Red and Blue Rescue team, two dungeons that have 99 floors, keep ruining your items with traps, and have strong Pokémon. To take it up a notch, there are 99 floor dungeons that lower your level to level 1 (Wish Cave and Joyous Tower in PMD1 and Zero Isle East in PMD2). To make it even harder, there are 99 floor dungeons that lower your level to level 1, do not let you bring any money or items, and do not let you bring in any team members, essentially putting you in the mercy of the random number generator (Purity Forest in PMD1, Zero Isle West, and Zero Isle South in PMD2). Explorers of Sky essentially just decided to make the hardest dungeon possible by making it 99 floors, lower your level to level 1, does not allow you to bring in any items or money, prevents you from bringing any team members, and keeps traps hidden after you trigger them. Explorers of Sky adds a new infair trap that warps and gives all wild Pokémon on the floor the "Grudge" status, which results in all power points of the last move used being drained away if you kill them.
FTL: Faster Than Light is in short, Star Trek: The Rogue Like. Even on easy it's still extremely difficult, with luck playing a heavy role. Run into a ship you're not well prepared to face? At best, you can expect to take hefty damage before you can escape. At worst, it's possible to die in the first sector.
Spelunky is an addictive platformer/roguelike hybrid in which you will die many, MANY times due to frogs, spikes, yetis, and everything in between. The fact you can make shortcuts to later parts of the game doesn't make the game any easier, only more plausible to actually beat.
The shortcuts actually make the game significantly harder. Since you then have fewer floors to get the items necessary to make winning the game plausible. The shortcuts also preclude you from entering the bonus dungeon.