This is one of the most popular roguelikes and is notable for having been developed by a team who mainly contacted each other over the internet. The fact that the devteam1 were from several different countries perhaps helped the games eclecticism and bizarre sense of humour.
For example, a knight might be riding through the dungeon when he comes across a fountain, into which he dips his longsword, which is then transformed into Excalibur. Then he sees a yellow light coming down the corridor, so he whips out his trusty towel and wraps it round his head, so as to avoid being blinded when the monster explodes. Removing his towel he spots a wumpus and, deciding not to risk his mount, he gets off to be told "You've been through the dungeon on a horse with no name."
What's it all about then?
The main aim of the game is to retrieve the Amulet of Yendor from deep in the dungeon, but the general idea is to collect useful stuff, kill hostile monseters and generally head deeper. On your way down, you will encounter a few branches off the main dungeon. These are a good source of useful objects and some are necessary to complete the game.
Shops are also useful places to find things, though the better items are generally more expensive. Don't annoy the shopkeepers, though, they're better able to defend themselves than the bloke in your local offy. Sacrificing at your god's altar will eventually2 produce results, too.
NetHack has spawned quite a few spin-offs, most of which influenced the developement of the main game. To name a few: NH+, NH++, NH--, NH: The Next Generation, Allegrohack3, NewtHack, GnomeHack, QtNH, SLASH4 and the seminal...
Originally the Extended Magic version of SLASH, this game first made the wizard a good character to play. SLASH'EM is currently most notable for its techniques, which allow Dwarves to do their impression of the Incredible Hulk (though they don't burst out of their shirts) with Rage Explosion, Monks to do lots of cool things by channeling chi and other races and classes to do all sorts of stuff. It also allows you to play vampires, which are pretty tough, but cannot get sustenance any other way than drinking blood, which makes playing one a desperate search for the next meal.
STOP PRESS: SLASH'EM now also has really fancy graphics, at least the Win 32 version does, can't vouch for the others. Unfortunately it seems to have more than its fair share of undocumented features5, so you might be better off sticking to an older one.
Go and play it
Like most roguelikes, NH and SLASH'EM are completely free, so go and download them now, they only take up a meg and a bit.