dtgreene: I could also mention Rogue. From what I hear, that game is short and lacks a save feature; however, it is quite random and you need to have some luck to actually win the game.
If you like ASCII roguelikes, you might want to check out Rogue, the game that the genre was named after.
IAmSinistar: Roguelikes are only short when you die. :)
Most games, if you can avoid death, will last quite a long time. The endpoint in them can take months of grinding to reach. The only one with a hard time limit is Larn, in which you need to recover a potion in time to heal your child. And even there the time limit can be extended through certain means.
I'm a fanatic for the original roguelike text games (my favourite flavour is the Angband series, especially
ZAngband). They have tons of replayability and can last for ages.
I am talking about Rogue in particular; from what I have read, the game is actually quite short even if you manage to win.
I have also seen the term "coffee break roguelike", which refers to some other very short roguelikes, which can be beaten in under a half hour.
Anyway, if you are into roguelikes, it is probably worth playing Rogue just to see how the genre started.