The Kindle’s focus on text and its crisp display would seem to make it the ideal platform for Interactive Fiction (IF), and one wishes Amazon would lead at least an experimental effort in writing the software to make this happen. As it is, however, the job has been left up to hobbyists and enthusiasts, and most of these projects are still in the early-germination stages.
Parchment and Portable Quest are two sites that allows you use IF stories (Zork, et. al.) in the Kindle’s browser. The experience works fairly well, but you have to be online to use it. KIF, ZMPP, and other projects hold out the possibility of Inform and TADS softwares on the Kindle, meaning you could download stories and use them offline.
The day when these will be useable is still a ways off. Even then, the ways and means of getting stories into users’ hands will probably need too many steps for things to really take off (a problem common to all modern IF efforts). Still, however, it promises to be fun to tinker with.