I like the tactical / strategic aspects to roguelikes. Though the AI is pretty (extremely) simple and the game is fairly basic in terms of options ...
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This is an aside. Most roguelikes have very limited options. You move, you wait, you attack (ranged or melee), you use a consumable. They're always dressed up, but they're not complicated at the core. Not that most games are, really.
... there is in fact a lot of depth. The resource management is incredibly important. The identification portion of the game is incredibly important. In games like Crawl there is an overarching strategy that you have to consider. Strategy that is derived from information learned within the game (I can't kill orcs easily, maybe I shouldn't go into the orc mines yet), from outside the game (various forums / threads / irc / etc that give you spoilers) and from personal experience.
That's the number one thing. I find there are very few games that have that kind of strategic and tactical depth.
Beyond that the randomization is key. Every game is different. If games were the same, you would get bored playing them over and over again. I don't understand people who replay games 2-3 times in a short span. I don't find that fun anymore. When I run out of new content, I'm done with the game.
Contrary to my point about randomization - I love Crawl's vault system and recurring content. It adds a lot of flavour to the game, and seeing a vault for the second or third time and thinking back to the first time you saw it, is a lot of fun. The key though is avoiding TOO much repetition. (I think Crawl has a bit too much in certain spots, particularly the Lair:8 and Snake:5 endings.)
Permadeath is very important. It ties into difficultly. Having just won a roguelike for the first time ever, I can say with conviction that it was the best feeling I'd had after winning a computer game. It felt like a real accomplishment. Without permadeath that wouldn't be the case.
In terms of the graphics... I don't like ASCII but I'm not hugely averse to it. If there is a graphical version available as with DF or Crawl, I'll play it. If there's not, and the game is worth it, as in case of Crawl online, I'll play that too.
One of the biggest things for me is the interface. Crawl's interface blows most roguelike, and non roguelike, interfaces away in terms of flexibility and ease of use (ok, ease of use is not quite as easy as for example DAO or some other semi mindless game).
edit: and I don't give two shits about story in the vast majority of games. If the game centers around a story, I want it to be good, but if the game doesn't, I'm cool with that too.