I wonder how many people like the idea of playing a game and when you die or lose to another player you have to start all over again...

It could be anything, a strategy game... an RPG, etc.

How long should the game be able to go?

Should there be so much to do that you will probably never reach the end before you die but still have the hope and the astonishment if you do reach it?

I think it'd be pretty cool to have an RPG or something that if you did reach the end game you looked really cool, had a hell of a bounty on your head and were well respected for your accomplishments, but could lose it if people killed you (which would be difficult to do). What I was thinking of doing to accomplish something like this is to have some sort of rune system. Like say there's 7 runes out there, each one requiring 1-3 days play and a 10% chance you will succeed in getting it each time you try. Once you acquire it, and you die the runestone will disapear, and whoever killed you will be rewarded with only small remnants of the power which the runestone gave you (and for say only a short period of time, like a day or 2) which would give them an upper edge still. The runestones could be things like granting you regeneration even while fighting (making it difficult for just one person to take you down), the ability to fly over objects... etc.

To not make people start completely over, you could have "checkpoints" where if a player reachs level 50, they get a marker that allows them to start level 20 characters for now on... so they don't have to go through the tutorial parts of the game.

Of course you'd have to make sure that the time investment wasn't more then a few days to reach the end game, but instead require more skill and intelligence to reach it... perhaps through puzzles and traps and such.
Permadeath is odd. Some people like it, it makes the game more dramatic, some hate it, it makes it too dangerous.

I don't like it personally, but it depends how difficult the game is. If the prime source of difficulty is other players, you may have problems. Think annoying player-killers are a problem? Wait till you have permadeath.

Probably better to have a permadeath/nonpermadeath option on character creation, and give permadeath characters a boost. Or rank them on a different ladder. Or something. Like Diablo 2, I suppose.