During its 30 year existence my firm had quite a few logos. Many were BCE (Back in Caveman Era) and I had to photograph my business card collection to show you those. As you can see many of the versions were driven by a change in the name of the firm. These changes were mostly perfunctory. BCE a logo didn't have the visibility that it does now. Most people didn't see it until you handed them a business card, or sent them something in the mail. Email was ACE (After Caveman Era) so you didn't send out much promotional mail after a while because you eventually realized the time and cost that you were expending was delivering zero results. It turns out that people don't hire an architect because they get a piece of mail.
So when BCE ended on April Fool's Day in 1996, we got busy. Architects like the golden section, so we didn't have to think about shape. My favorite color is green so that was simple. All those names fit better on a vertical rectangle - WOW, that was easy!
Once ACE got rolling, websites added a new wrinkle or two. Nothing that was unmanageable. Social Media on the other hand ...
It became obvious pretty quick that Social Media did not like vertical - at all. Tumblr, nope. LinkedIn, nope. Twitter, nope. Facebook, nope. Google+, nope. Even non-Social Media sites like Basecamp are not very permissive about shape when you personalize. In fact square is the clear winner / preference. Social Media definitely is fond of anything square or round - or square. Maybe that is because the majority of the big boys use a square or something very square-like. This graphic that's making the rounds demonstrates that point; and, as a bonus, gives you a lesson in color selection for your new logo project.
Even a favicon, that little doohickey to the left of the URL is a square. 16 pixels by 16 pixels is the specification. We never did catch on. There was always a new place cropping up to add our logo. We should have stopped experimenting when we got to the first one in the second row up above.
You might have an ironclad reason for going off-formula; but, barring that, go with a square logo and save yourself a lot of aggravation.
Graphic credit: Thelogocompany