When I was in college, various of these games were mini-obsessions and I dubbed them "drop-out-of-college games". I first started with Nethack. Nethack's basic premise is that you've been dumped into a dungeon and you have to descend to the bottom (past many perils) to retrieve the Amulet of Yendor. This is actually the same premise as the original roguelike game, Rogue, which may account for some of Nethack's popularity. There were some things I really liked about Nethack, but after countless hours of gameplay, I discovered even more things that I didn't like. There are some elements of the game which I find silly. For instance, while I understand that "things rust" is a fact of life, it's not necessarily a fact of life I want to deal with when I'm playing a game. And if I'm dealing with it, it stands to reason to me (and probably to me alone) that artifacts, ultimate magical weapons or armor of great power and might, should be exempt from this fact of life by default. I mean, if Excalibur isn't always rust-proof, how did the Lady of the Lake keep it intact all those years? Despite these quibbles (and many others which I won't detail here) Nethack is essentially a fun game. Avoid getting too attached to your character, and you'll have a lot of fun and even a lot of laughs.
After Nethack, I turned to Angband. Angband loses a lot of the silliness that some people love in Nethack, and has a very different "feel". The objective in Angband is to defeat the Ultimate Foe, Morgoth. Those of you familiar with Tolkien will recognize both Angband and Morgoth as Tolkien creations. In theory, the game is based upon Tolkien's universe as described in The Hobbit, The Lord of the Rings trilogy, and The Silmarillion. In practice, but for a few uniques and artifacts there's not actually a whole lot of Tolkien in the game. Unlike Nethack, you start the game not actually in the dungeon, but above it, in a town. In the town are a few shops, townspeople (who will drool on you, beat you up, or try to steal stuff from you), and your home. The dungeons in Angband are completely random - every time you go down to a level it will look completely different than the last time; this is justified by the vast size of Morgoth's domain. This changes the dynamic of the game dramatically from Nethack. You have nearly unlimited sources of dungeon-exploring supplies in the town, you can store many things in your home and get them later, and every time you descend down from a level, you know that coming back up you will have to explore it again just to find the stairs. Angband has inspired many many variants, and I've spent a while addicted to a few of those, too. The original Angband (or "vanilla") is still my favorite, though.
Speaking of Angband variants, Oangband (the O stands for "opinion") is a pretty darn neat one. Some cool things that Oangband adds to the Angband mix are: a quiver slot for ammunition (you wouldn't believe how useful this is), a revised combat system, and more detailed descriptions of items and monsters.
Another Angband variant which I've played and enjoyed is Kangband. Kangband adds user-definable quests to the Angband pot-luck, and some different races and classes as well. There's also a wilderness outside the town, and more buildings in the town. There's an arena, in which you can fight critters, and guild halls which are highly useful to different class characters and even non-class characters. There are also some terrain features in the dungeon itself, which spice things up a bit. Unfortunately, I got distracted from kangband by some other games and didn't get to explore too many of the different classes and races, but now that I think about it... ~grins~
No list of neat Angband variants would be complete without a mention of Zangband, or Zelazny Angband. Zangband takes critters and stuff from Roger Zelazny's Amber series and adds it to Angband. Also, the magic system is based upon Master of Magic (a favorite non-roguelike game of mine... I'm actually HTML-izing a faq for MoM currently). These changes, along with a very extensive wilderness with many towns, quests, extra character classes and races, make Zangband a lot of fun to play. In addition to poweful Amberites, you'll also encounter creatures from H.P. Lovecraft's stories (I have yet to fight "Azathoth, seething nuclear chaos", but I'm not looking forward to it) and, if you choose, some silly creatures like Santa Claus, Godzilla, and Barney the Dinosaur. You also have a chance to get mutations, either by serving a patron who wumps you with one (getting the message "you have a hallucinatory insanity" when you gain a level is not fun), or by paying to be exposed to chaos and take your chances with a mutation. There are all kinds of neat things in Zangband, from magical statues to different kinds of armor and equipment. I really like this game.
Adom is another popular roguelike which I've indulged many hours in playing. Ancient Domains of Mystery is a good game, which used to suffer from some pretty major bugs. Thankfully, most of those seem to be cleared up now. The game is much more plot-driven than other roguelikes; there are multiple endings to the game depending on how you play and what your goals are, but the basic and (allegedly) simple goal is to keep the world from being flooded by chaos. In order to do this, one must shut the chaos gate. There are many small but highly challenging quests you must complete along the way (and many optional ones as well). The game has a skill system, sort of like crawl. In Adom, however, your skills primarily improve when you gain enough experience to get a level, and then they improve by a random amount (3d3, for instance). There is a definite time constraint on how long you can just mess around before you need to get moving on the main goal of the game, because after a certain point you start to mutate (due to the increased chaos in the world) and too many mutations means death. As in Zangband and other games with mutations, some are good and some are bad. If you're looking for a more "directed" kind of roguelike, this is the one I'd recommend. The class and race combinations are varied and offer some interesting options - for instance, playing a bard is a very different game than playing a fighter, and playing a troll is worlds different than playing an elf. In many ways, these differences are more pronounced in ADOM than in other roguelikes which also offer a range of class and race combinations because of the skill system, the plot, and the importance of alignment. ADOM has even more replay value than many other games, because even if you've managed to win (and it is quite challenging), you've still only won in one way, with one particular kind of character.
So, there's a list of the roguelike games I've invested way too much of my time in. Hopefully, someone else browsing through will now a) know what the heck the "angband equipment chart" and "crawl hall of fame" links are for and b) find somethng fun and addictive to play. Enjoy!