Narratavius is an app which allows you to play interactive fiction stories, also known as text adventures. Where Narratavius differs, though, is that it was designed from the ground up to run on iOS. Instead of typing commands into an on-screen keyboard, you will simply tap to make decisions.
Narratavius supports independent authors, and its stories can be written to fall in any genre.
Narratavius currently comes with one story for free, and others may be purchased using in-app purchase. Both the free and paid choices will expand as new versions are created!
You can learn all about Narratavius at its website: http://narratavius.com.