Great article. However, I don't feel what you're describing ascribes to specifically, a horror game. If there is no victory in a videgame, it defeats the entire appeal of playing a videogame: interactive escapism and catharsis. 

For movies, it's fine to have the characters fail over and over (Requiem for a Dream). But when such failing is interactive, more people will be annoyed and feel they've wasted their time. Negative reinforcement can only go so far. 

However, there are some videogames that don't end in happy endings. [b]Kane and Lynch[/b] is a game where you play as criminals, who get stuck into one mess after another until the very end, and there's no real victory other than you completed the game. It's as close to playing an interactive nightmare you'll get, where none of the characters are particularly likable, and nothing good ever happens. If you want another nightmare game, check out [url=http://www.youtube.com/watch?v=6NLSHOpvkNw]Darkseed[/url], a MS-DOS game on the PC. One of the scariest games of all time. [b]Condemned: Criminal Origins[/b] has you as a cop who starts going insane throughout the game, and ends with you lost in your nightmare hallucinations. [b]Call of Cthulu: Dark Corners of the Earth[/b] has you playing a detective back in the 1920s where you know your character will eventually commit suicide as foreshadowed in the opening. 

There are a few videogames that play up the disempowerment aspect, like [b]Far Cry 2[/b] where your weapons can jam or blow up in your hands, so you can be in a situation of no hope leaving you to either get to a safehouse or weapon shop with just your secondary weapon and a knife. [b]Metro 2033[/b] can have you trying to survive just at the very edge, where you're trying to live on your gasmasks in the irradiated post-nuclear ruins of Moscow. 

Have you played Passage? Not a horror game, but it sounds like exactly what you want to see.

Roguelikes fall into the camp you describe. In there, there is permadeath - i.e. you die and your save file gets deleted, with only a tombstone and entry in the high scores to remember that particular character by. Of course, you can start again with a new character, but since most Roguelikes are procedurally generated, the fact you've played before won't necessarily help you. In fact, it probably won't, since the mysterious words on magic scrolls mean different things from game to game.

I've had one of my favourite ever experiences playing Angband. I was down to the fifth or sixth level of the dungeon - further than I'd ever been - and suddenly, my torch ran out. I was plunged into darkness. Because Angband only uses ASCII characters as graphics, this just meant I couldn't see monsters approaching on the map, and the map itself didn't update until I hit a wall.

So I had to find my way out by "feeling" my way along the walls - i.e. bumping into them - until I found the way out. And I did, despite being attacked in the dark several times. It was a thrilling, scary experience that didn't require any graphics to be tense - just the feeling that "this could go HORRIBLY wrong at any moment".

Interactive fiction titles, too, aren't afraid of allowing you to take an action that will cause you to be unable to succeed. Depending on the "Zarfian Cruelty Rating", this may or may not be apparent to the player until much later.

Heavy Rain, being essentially an interactive fiction title with graphics, also allows you to do this. The story continues even if one (or all) of the characters balls it up partway through. (Spoiler?) There's even a Trophy available for getting all the characters to the finale and then STILL cocking it up.

Also, EVE Online is world-renowned for being one of the only MMOs to take this business seriously, too. Jump into unsecure space and into the middle of a pitched battle and there's the distinct possibility you could lose MONTHS worth of play time. Your character won't die, but you'll just lost a TON of stuff.

Similar to the roguelikes Pete mentions, I was going to bring up Demon's Souls, but of course, even that you can win. I disagree, however, with Moeez that "not winning" negates the escapist intentions of the medium, specifically because  it happens in other mediums all the time. That Requiem for a Dream does not end happily doesn't ruin the experience for me.

But this happened in early games, all the time. You can't "beat" Pac-Man or Donkey Kong in the same way you can "beat" Mario. You can only do a little better, each time :-)

And I haven't played it yet, but does Heavy Rain fulfil what you asking for, in that the game can end in such a way that you don't win?

@Paul That's not entirely true. The Passage is about reflecting on life, yes, and it isn't a power fantasy by any means. However, it does in fact fall victim to the same mechanics Gerard mentions -- yes, you die, but you do not lose. When you die you've reached the end of the game as intended, and therefore have "won" the game.

It's difficult, then, to work around Gerard's thesis. Let's assume that a game exactly like Super Mario Bros. is created, but in the final dungeon, or even the first one, the game was intentionally created so that beating Bowser was impossible, and that there is not an "end". Is this a valid example of what he wants because we cannot "win", or is it not because we've technically reached the "end" of the game?

Perhaps I'm confusing intention of loss and actual loss? Perhaps a horror game where the end of the game comes suddenly from a random event in what seems like the middle of the game is an example.

@Ben: Yes. Without spoiling anything, Heavy Rain has a number of endings which in traditional game terms are "failures". But they're still endings. You've still beaten the game. It depends what you mean by "win".