Designed by: Jay Fenlason, Andries Brouwer (original Hack), Mike Stephenson, Nethack "Dev Team" (Nethack), many contributors
Influenced by: Rogue, Hack, D&D.
Series: Just the one, although I suppose one could count variants as being of the same "series." In that event: Nethack TNG, Nethack --, Nethack +, Lethe Patch, Wizard Patch, SLASH, SLASH'EM, Sporkhack and others.
Legacy: Diablo and Diablo II were not directly influenced by Nethack, but they share Rogue as a common ancestor. A long-lived JRPG series, Mystery Dungeon, is informed by Nethack's design strengths.
For useful background information on the concept of a "roguelike", check Gamasutra's earlier article on the topic of Rogue.
Above, in the section on Wizardry, I remarked that the biggest thing that pen-and-paper RPGs had, and still have, over CRPGs is lack of flexibility. The player characters cannot do everything they could in a real situation because the computer cannot generalize the environment to the degree that this could be done, and doesn't have the creativity to improvise things in response to player actions.
The standard CRPG method of dealing with this is to provide the most important and obvious actions: Move, Attack, Search, Eat, Rest and stuff like that, and to specifically reduce the importance of other things. Nearly always this results in a game world that's lacking in scope for player action, since a truly ingenious player can often come up with something bizarre and useful to try.
The only RPG genre to make any headway against this long-standing limitation of the form is the roguelikes. Of all of them, they're the one to have overcome it the most. Indeed, the shining beacon that shows us that after all these years the problem may yet prove not to be completely insoluble is Nethack.
Nethack's solution, admittedly, may not be universally applicable. It solves the problem of players not being able to communicate what they want to the game by giving them an over-abundance of options, and it solves the problem of not offering players things to do with those options by using a lot of random content generation, hidden uses for abilities, and being content to let a few of those commands be usable only in occasional instances.
On that first problem, about communication with the game: Nethack has dozens of commands. Players can sit down, throw or wield anything they can carry, dip objects into potions, fountains or standing water, write on the floor, play musical instruments, disarm and reset traps, make offerings to the gods, and many other things. Not all of the commands are needed to play through the game, but Nethack's game universe is complex enough that the best players know them all, and know when they're useful.
On the second problem, that of what to do with the options allowed, it uses a lot of knock-on monster and item properties. Every item has a composition; things made of paper could be burnt by fire attacks, those made of metal rusted by water.
Monsters which are orcs automatically take extra damage from the sword Orcrist. Monsters with sight can be blinded by expensive cameras. These incidental properties provide a fair amount of Nethack's depth. Interestingly, they don't come as a result of an object-oriented design. Nethack is implemented in straight C, with nary a class statement to be found!
Nethack is a roguelike, and so I'm required to say something about one of those games' most controversial features: permadeath. (Okay, I admit it -- I've been leading up to this.) Since Ultima and Wizardry, but unlike pen-and-paper games to this day, players are allowed, and even encouraged, to save games and return to them if things go badly, a design characteristic that makes it almost impossible for anything really bad to happen to the player's characters.
I make no secret the fact that I consider this one of the most pernicious aspects of CRPG gaming, that permanent disadvantages acquired during the course of play cannot be used by a designer because the player will simply load back to the time before the disadvantage occurred. Admittedly, the prevalence of this attitude comes from some older games that could easily be made unwinnable if the player wasn't careful.
However, it's reached the point where "adventuring" in an RPG rarely feels risky. Gaining experience is supposed to carry the risk of harm and failure. Without that risk, gaining power becomes a foregone conclusion.
It has reached the point where the mere act of spending time playing the game appears to give players the right to have their characters become more powerful. The obstacles that provide experience become simply an arbitrary wall to scale before more power is granted; this, in a nutshell, is the type of play that has brought us grind, where the journey is simple and boring and the destination is something to be raced to.
Nethack and many other roguelikes do feature experience gain, but it doesn't feel like grind. It doesn't because much of the time the player is gaining experience, he is in danger of sudden, catastrophic failure. When you're frequently a heartbeat away from death, it's difficult to become bored.