More on what Angband is at http://www.thangorodrim.net/ and http://angband.oook.cz.
I finally beat the game, by killing Sauron and Morgoth.
My character dump is here.
I've been playing Angband on and off for years now, longer than I've been playing Starcraft. I've never before come close to winning, let alone actually winning.
In Angband, as you go down into the dungeon, the monsters around you get much, much stronger. How strong you are is based on your level, your stats (which can be increased, but max out at a point), and your equipment (armour/weapon/consumables like potions of healing and scrolls of teleportation). Everything is based on randomly generated stuff, in randomly generated dungeon levels. You may be overpowered vs the monsters at 500 feet deep, and have no chance against the average monsters at 1000'. After a certain point, there are many monsters who under certain common circumstances, can kill you instantly.
Therein lies in how angband is hard. It can take a long time to dive into the dungeon, collecting awesome weapons, armour, getting a nice cache of support items and consumables, killing unique monsters (like Saruman, Smaug the Golden, Smeagol), finding artifacts (like the phial of Galadriel), leveling up (to a max of 50), maxing out your base stats (to 18/100), and you can die in a very short time. When you die, you're really dead. Your character is just, gone. You have to start all over from the very beginning, with completely newly generated dungeons, where you'll find different monsters and items at different times. The only thing your character passes on to your new character is its monster memory, the stuff you find out about monsters (e.g. Sauron resists all elements except acid, a vulnerability you can exploit) as you fight them. Now, combine a long game, largely based in luck and chance, throw in monsters who can be a challenge even after you've beaten Morgoth and the game, and plenty of ways to die instantly, and you have a very hard game.
A few classic ways to die:
(upon generating your new character) The Battle-Scarred Veteran hits you! You die.
(upon entering a new dungeon level and taking a single step) The drolem (offscreen) breathes poison! -more- You die.
(battling a unique dragon, he's at full hp) Kavlax the Many-Headed breathes gravity! You feel gravity warp around you! -more- You die. (atleast you can get resistance vs poison, vs gravity, you cannot; breath-based attacks are based on hp: more/fuller hp, more damage)
I love the game, I encourage everyone who has the time to play it, but it's really hard.