The story has to keep me engaged, not only while viewing, reading, etc, but also after finishing a chapter or episode. I want to be challenged as a consumer and I also want the story to be thought-provoking- whether that be reminiscing on hilarious moments, thinking of "what if" scenarios, putting myself in the position of various characters, giving me ideas for stories, etc.
But while actually reading or viewing, I just need to have a reason to invest my time in the story. The story has to offer something that I love or something new because I can easily just read or watch a myriad of other things.