I have never thought of using a square format, until today. I have known of the phenomenon Vivian Maier, an accidentally discovered amazing street photographer, during her life time she had took over 100,000 photos but none of it was ever shown, until around of her passing.
To my understanding, at the end of her life she had not kept up with the payment of her storage space and subsequently all of her belongings were auctioned off. A few bidders bid and won her belongings. One of the bidder Mr. Maloof did a lot of investigations and was the person who brought her work to the world (not sure if she would have appreciated though, as she was known to be a bit of a loner).
Anyway, there are plenty of reviews and documentaries on the web and YouTube, it is definitely worth a look!
The only square format I have even known is of the Instagram universe, and I have always found it quite awkward to work with, until I see her work :-)