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Wikipedia defines a Roguelike as

The roguelike is a sub-genre of role-playing video games, characterized by randomization for replayability, permanent death, and turn-based movement. Many early roguelikes featured ASCII graphics. Games are typically dungeon crawls, with many monsters, items, and environmental features. Computer roguelikes usually employ the majority of the keyboard to facilitate interaction with items and the environment. The name of the genre comes from the 1980 game Rogue.

I have slightly different viewpoint here.  The wikifinition is well and good, but lacks a crucial element I feel all in the roguelike category share.  What you have there is the cold definition – but what’s most important is the sense of adventure they convey.  Typically the mechanics are dated, the graphics are quite trash, and the sense of atmosphere (or environment) is non-present – but the feeling of adventure is total.  You never know what might be around the next corner.