Many sites offer stories, essays and articles to read or download in the Hindi language. Google Books is a good place to start, simply type in your preferred subject in the search engine and see what it comes up with.
Of course, which sites you'll wish to visit depend upon which subjects you are interested in. The panchatantra stories, moral stories for children (pictured), are available via an app at: 1mobile.com/panchatantra
and apps.hinkhoj.com, or online at indif.com/kids/hindi_Stories or hindikibindi.com.
Free Hindi Stories for Adults
You can find ghost and horror stories in Hindi at indianghoststories.com, and adult Hindi love stories at antarvasna.com. You can a selection of horror and adult stories, as well as thrillers and romances in Hindi, at hindinovels.net and freehindibooksforyou.blogspot.com.
For shorter articles or essays in Hindi, search through shareyouressays.com or scribd.com, though you may have to join these communities before you can download an article.
There are also many stories in Hindi, including Bible tales, motivational stories and children's stories, available on YouTube, such as this panchatantra tale: