I chose to focus primarily on 2 games and their variants: Nethack and Angband. Each one has a very distinct playing style.
Nethack
In Nethack you choose your character’s race, gender, and class (called “role” in Nethack). The standard game offers 13 roles to choose from, and 5 races. While one role is restricted to females, the others can be played with male or female characters. The role you choose affects which races you can become. You’ll start off equipped with some useful items, a weapon, and armor. As your character gains levels, they get abilities (some right away) that are unique to each role. Learning how to use those abilities will improve your chances of survival.
The roles are: archeologist, barbarian, caveman, healer, knight, monk, priest, rogue, ranger, samurai, tourist, valkyrie, and wizard. The races are the usual fantasy ones: human, elf, gnome, dwarf, and orc.
The way to win Nethack is to journey through a dungeon of 50 levels, find the Amulet of Yendor, bring it with you back to the surface, ascend a few more levels, and offer it on an altar to your god. This, of course, is far from simple. Becoming better at Nethack involves learning the uses of anything you are carrying (including some far from obvious uses), interacting with the features and inhabitants of the dungeon, and trying not to make mistakes. Because it is turn-based, you should think about your options carefully – that vicious monster won’t move while you check your inventory.
Nethack includes a “Guidebook” of 62 pages, and an in-game help system. The Guidebook has a lot of useful information and hints to help you play the game, and reading it before you begin play is definitely recommended. The game is very hard even without making use of other sources of information about the game (termed “spoilers”).
Nethack can be played using ASCII characters

Priest – Nethack with ASCII
or with tiles enabled:

Priest – Nethack tiles version
If you play on a Debian-based Linux system, the “Documentation” section of the repositories will have a spoiler file.
Nethack is considered to have 3 stages of game progress – early, middle, and late – determined roughly by what area you have reached in the game. Your short-range goals will change from stage to stage. It seems to be the consensus among the better players that the roles also fall into 3 groups: strong in the early game, weak in the early game but becoming excellent in the late game, and weak throughout the game (yet still able to win).
It is a single player game, but most variants (and the vanilla version) let you play online using a telnet client to sign in and play. You can watch other people play, see high scores, and others will see your progress. The only thing you can’t do online is use a “tiles” version of the game.
Nethack doesn’t have a town level, and each dungeon level is preserved while playing the same game. Unless you look up spoilers, you’ll be taking a lot of notes about monsters and their weaknesses, special levels of the dungeon and how to reach them, and what items are the best ones to keep with you for use later on.
There are less than 10 Nethack variants, some of which are no longer active. The Nethack wiki has a list of all of them.
Angband
In Angband you also choose your character’s race, gender, and class. The standard game offers 11 races but only 6 classes. The classes are Warrior, Rogue, Mage, Priest, Ranger, and Paladin – much more “standard fantasy” types than Nethack lets you play. When you choose your race and class, the game shows you how your attributes are affected, and any advantages or disadvantages you have.
Your choice of race has no effect on which class you are allowed to choose.
Angband doesn’t have a Guidebook, but an FAQ mentions the 2 primary websites for it: rephial.org and angband.oook.cz. The forums, and a list of variants are at the second link, while rephial features a link to spoilers and an outdated but still useful Players Guide.
Two of the big differences between Angband and Nethack are the town level at the top, and the fact that when you leave any particular level, it is lost. Returning generates a new level, new artifacts, and monsters. You are expected to return to the town every so often in order to buy scrolls, better weapons, etc (town portal scrolls in Diablo are definitely borrowed from Angband). Angband is generally considered to take longer to play through than Nethack. It is more of a combat-oriented game, with very few puzzles. Because of the way shops work, stealing from them is impossible; in contrast, good Nethack players have learned the benefits of stealing from shops they find (one of the benefits of keeping your pet around!)
The levels in Angband are also much larger than those in Nethack. Nethack levels always fit on one screen when using the ASCII graphics, while Angband’s sprawl all over. There’s a command to see the entire map at once, which will also show you any stairs found. Hunger in Angband is much less a focus than it is in Nethack – monsters won’t leave corpses, and you must buy your food.
The number of Angband variants is much larger than those for Nethack – many are no longer being maintained, although they are still playable. The Angband forums has a Variants subforum that seems to consider less than 10 variants still current.
Playing online is pretty well supported in all versions of Nethack, while I don’t really see it as an option for Angband. I’m planning a post specifically about online play, where I will go into more detail.