Diablo 2 was, as far as I know, the last really popular permadeath game. Originally role-playing games drew inspiration from life and from wargames. In both of those your unit (sic) is extinguished once killed, dead, gone, game over. Over time it's suited both players and developers to allow play to continue past moments of losing. (In fact in single player games people almost always reloaded when they lost anyway even if it did feel a bit like cheating).
So why would anyone want to play hardcore? Is it just masochism?
I think to best understand it one needs to step back from immersion. Sure, some people like it that their character plays a story with closure. My old guild had a subforum devoted to death reports which turned into a remarkable place with friends paying tribute to other people's characters and even our own resident elegist. The key to understanding hardcore, however, is to look at the game mechanics.
So what are the game mechanics of hardcore? It's harder. It forces you to always focus. That can be very compelling. It's stressful. It's challenging. It resets your character from time to time so you can start over. Other people do less well, no one bad is going to be ahead of you simply by having spent more time. Grouping is a massive exercise of trust. Good groups feel awesome (since your trust proved well-founded). And beyond the beginner areas you never group with a bad player (although malicious players are possible, nobody is actually bad).
So it's all about the tension between risk and reward. Having to pay attention means you are more immersed in the game. Having to minmax your survivability makes you better at strategising a character build. The stress of the danger is exciting - sometimes your body will respond to the game, your pulse races, you sweat, you curse out loud. (Reading that back that sounds super-nerdy, let's move swiftly on!)
Viewed in that light it's very clear that hardcore is just right for some players and not right at all for other players.
So how do you know which you are?
Well, try it. And not just once, try it from time to time. My first go at Hardcore I couldn't get out of Act 1 Normal in Diablo 2 so I shelved the idea for several months. Later on I tried it again simply because softcore didn't feel challenging enough. Once I'd played hardcore for a while softcore became unthinkable, as bland as playing Windows Solitaire.
With Diablo 3 I see the auction house as a new frontier. So even though I would naturally incline to Hardcore mode because the Real Money Auction House is only for softcore I'll be playing there. And it's not just about the money, it's about the gaming of the AH. It is a very interesting and of course a fiercely competitive minigame.
So what if they extend the Real Money Auction House to Hardcore? I'll definitely move over. I think it's a much more exciting way to play and I also think it will be more lucrative. Hardcore mode has two elements that really ramp up a game economy - item destruction and challenge. People will be obsessed with beating Inferno and some of them will spend a lot of real money to try to do so.
So that's my decision - softcore until a Hardcore RMAH is released then hardcore. With 2 weeks to go, have you decided which mode you want to play Diablo 3 in?