There are two things that make Nethack truly special (well, okay, roguelikes in general, but Nethack is the best of the lot...ADOM would be a contender if it were actively maintained...but it's not).
1) The first point is the one I've always been able to express. Namely, every game of Nethack is different. Since I've said this before, I won't belabor the point, but just in case there are people reading this who've never even heard of the game before, I'll elaborate enough to be clear.
Every time you play, every level, and even which levels appear in what order, or even appear at all, is hugely randomized. There are some consistencies in how various parts of the dungeon are structured, but all that does is prevent the game from feeling totally chaotic. No two games are alike. The items and creatures you encounter, the locations of exits, altars, kitchen sinks, and hidden closets, number of rooms, paths between them, hidden vaults, and even gold and gems embedded deep in the walls of the caves are totally random. On top of all that, the character you start with changes the game dramatically, and there are ~20 character classes, several races, three alignments, and two (count 'em) genders, all of which have a non-trivial effect on the play of the game. I randomize my character selection, so even THAT is never the same twice*. So Nethack never gets old. Fine. Who cares? Why is it so exciting that meals, friends, and ::gasp:: work become casualties in its wake? It's ASCII, for The Lady's sake. The answer brings us to my revelation:
2) Nethack is a constant walk along the tension of the fine line between life and death. Might sound like I'm being melodramatic, but I'm quite serious. You are always living on the edge. The thing about Nethack is that there is always at least one major thing going wrong. Even if you are in perfect health, and making good progress, you are constantly forced to think ahead to how you're going to get the next piece of equipment towards the "ascension kit" you'll need to win the game. And in solving one problem, you invariably create two more problems, often just as serious as the first. For example you suddenly realize those boots you just tried on hoping they'd be speed boots were actually fumbling boots, and they were cursed, so they don't come off. You finally find a fountain to dip them in to remove the curse, and dipping finally uncurses them...just as it produces a stream of poisonous water moccasins. Desperately reading scrolls hoping for a teleportation out of the mound of shit you're now under, you accidentally discover a scroll of earth, which crushes you, and each of the surrounding snakes, under your own personal boulder. You barely survive intact, but now you can't get out of the room, and your god is still angry with you for accidentally sacrificing a werewolf (forgetting that werewolfs are people too, and lawful gods are unamused), and with no pick axe and no rations, you're in a whole new kind of doo doo. And so it goes...
But as you're getting constantly shit upon by fate, your own stupidity, and the fact that it's just a damn hard game, you're also constantly gaining levels, finding artifacts of glorious power, and generally becoming so much of a badass that you really want this one to live to see another sunset at ground level. So every minute of the game is tense and exciting, trying to prepare for everything, because you don't know if the next bend in the passage will reveal the Vorpal Blade or the Jabberwock. (Yeah, they're in there.)
These aren't the only reasons this game kicks ass, and some would claim that there ought to be a "3) the dev team thought of everything", but these two are the two that keep me coming back for more. I'll die a loyal Nethack fan.
*kids don't try this at home. Play one class for a while until you know it, then move on to a new one. I know them all, so I'm in the clear.