Story Scenarios, unlike traditional Arkham Horror scenarios, play out more like a story (hence their name). Anyone who enjoys playing Mansions of Madness will enjoy playing Arkham Horror Story Scenarios. In fact, I was inspired by Mansions of Madness when I devised my story scenario system.
Most story scenarios don't involve the Ancient Ones or gates to other worlds. Instead, the investigators have a mystery to solve or some other objective or series of objectives to complete to win the game. Since the text for my Story Scenario system is too extensive to reproduce here, I will supply you with the following links to the files.
The Story Scenario rules:
http://www.fileden.com/files/2012/3/31/3285998/Story%20Scenarios.docx
And three sample Story Scenarios:
"Classroom Curses" (inspired by the Mansions of Madness story of the same name):
http://www.fileden.com/files/2012/3/31/3285998/Classroom%20Curses.docx
"Shadow Over Innsmouth" (inspired by the Lovecraft story of the same name):
http://www.fileden.com/files/2012/3/31/3285998/Shadow%20Over%20Innsmouth.docx
and "Ye Olde Magic Shoppe" (an original creation of mine):
http://www.fileden.com/files/2012/3/31/3285998/Ye%20Olde%20Magic%20Shoppe.docx