We owe it to each other to tell stories - Neil Gaiman
I had a quick look at Storify but with no real idea on what social story to pull together and a fleeting unease about using content from other people I've benched use of it for the time being. I can see how it would be useful - pulling together content on the same theme/subject from a variety of platforms (Facebook, Twitter, You Tube, Instagram) and having it in one place for consumption. If you were running or participating in a conference or event that encouraged the use of hashtags then you could find content to pull together and curate as a summary of the event. That would have the advantage of enabling information to be shared with those who do not use all or any of the social media platforms from which content can be pulled.
I think it's also a useful tool to enable people to catch-up on things they've missed or could not participate in (live Q&As on Twitter like the National Theatre's #askaplaywright).
I'll certainly be thinking about how I could use Storify in the future, whether for work or personal interest.