It appears iPhones weren't the only devices having trouble with the update, either. As Brianna Wu noted on Twitter, the update has also bricked her iPad Pro.
Apple, for their part, issued a statement saying: "We experienced a brief issue with the software update process, affecting a small number of users during the first hour of availability. The problem was quickly resolved and we apologize to those customers. Anyone who was affected should connect to iTunes to complete the update or contact AppleCare for help."
Of course, that's cold comfort for someone still staring down the "Connect to iTunes screen."