The basic idea has been something that's been around in gaming for a long time. Going all the way back to the PC game Rogue, you adventure for as long as you want but if you die you lose everything and need to go back to square one. This is something I love to see in games, I look for any game that has this feature to try out and see how hard it can be. Before I even knew these type of games existed I would play many of my old school games in this fashion. I remember playing may SNES games were I would start over if I died and I always play my scrolling shooters in this way.
The game that really showed me other people liked this concept was Diablo 2. It had the Hell mode where you lost you character if you died. I can't remember if this was in the first Diablo as I didn't play a ton of it due to hardware issues at the time. I was blown away they included this mode, it adds a tension that at the time I had never experienced in a game. Yeah I was playing games like that before but actually being forced to lose your character and start over was just awesome to me.
We're starting to see this type of mode in more and more modern games. Torchlight has it and games like Spelunky and Dwarf Fortress take the roguelike approach to them. One big name game coming out, The Witcher 2 has a mode like this. You can save as often as you want but if you die it's game over, I cannot wait to try this mode out it holds so much potential for a challenge.
I want to mention another game that didn't feature a mode like this but it has a following in the "no death run" method of playing and that's Far Cry 2. I loved Far Cry 2 even with it's flaws but this is an interesting way to play this game. Exploring the jungles and forests of Africa never sure if there's someone waiting in the bush to snipe you it adds to the game play. Add to this if you never buy the upgraded weapons and just use the crappy stuff your enemies drop and you have an experience a lot of games can't offer you. Another game series that get's ever more exciting to play with this restriction are the STALKER games. They're already pretty unforgiving so add in the fact that your first death is your last and you get a real sense of how brutal the Zone can actually be. Try playing Shadow of Chernobyl with one of those realism mods on Master difficulty and only give yourself one death, you'll be going through the game at a snails pace just fearing death. It's can be so much fun, I want to see more of this in gaming.
I would like to see more titles ship with this option. I don't think games should only offer this as a game play choice because it will turn off some players but I would welcome challenge and I'm sure there's plenty of other people who would love to see this too.