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Many text based RPGs today are dungeon crawlers that use ASCII text to display dungeons and towns. Dungeon crawlers are usually more action and combat oriented, rather than story driven, and a large emphasis is placed on collecting loot and slaying monsters. Examples of this sort include Akalabeth (the precursor to the Ultima series), and roguelikes such as Angband and Nethack.
Popular RPGs that use text-based graphics:
Akalabeth (1979) - Created by Richard Garriott, Akalabeth (later re-labeled Ultima 0) used text based graphics to display the world. The Ultima series would help define computer RPGs as a genre. Like many early text RPGs, it was combat rather than story oriented.
Rogue (1980) - This is the game that inspired the term "roguelike". Games of this sort usually involve dungeon-diving, and a focus on getting loot and killing enemies. They also typically include permanent character deaths, adding an extra layer of difficulty.
Nethack (1987) - Nethack is a roguelike that is still popular today, and is still in active development after 22 years, which is quite a feat for a free video game.
Angband (1990) - Angband is another roguelike, but it is set in J.R.R. Tolkien's Middle Earth. Games of Angband can take long periods of time to complete, as the player must traverse a randomly generated 100 level dungeon in order to eventually defeat the evil Morgoth. Like Nethack, Angband is still being developed.
Ancient Domains of Mystery (1994) - ADOM, as it is often abbreviated, is a roguelike with strong emphasis on character and story development, which makes it unique in the genre, as most roguelikes are combat focused.