Interactive fiction is text-driven games and stories most commonly associated with the dawn of the computing age and games like Zork. Depending on one’s definition, you might be able to stretch the category to include games like Nethack.
Today, it is a thriving sub-culture with new works being created by independent creators. The Interactive Fiction Database is a good way to find great games or genres. The Interactive Fiction Competition a good place to look for new works. For a gentle introduction, try one of the many guides available.
The game 9:05, playable via the link, is a commonly referenced entry point to interactive fiction and is also used by English as a Second Language teachers to teach basic English vocabulary.
If you’d like to go old-school, some have been made playable in a web-browser. Want to play Zork without installing any software? Now you can.
Or, if you want to get a feel for these types of games but still want some graphics, try Nethack, a dungeon exploration game with permadeath which has recently been updated. Easy to learn to play, but very difficult to master. “Internet user needs food badly!” Best played cold, but it is also interesting to play if you read the spoilers.