Apple - Is it normal for iOS updates to fail or to take hours on launch day?

This is quite expected for several hours (and sometimes even a day later at popular times like first thing in the morning) as Apple tunes the servers that host the download images. Usually, things smooth out several hours after the launch and if you have this issue for more than a day, I would contact support just in case it's your device that is having problems.

Even more important than the download servers are the activation servers that verify the software wasn't corrupted or tampered with as they seem to be preventing many people from updating even after the software is downloaded and installed on the device.

It's not unrealistic that thousands or even a million devices are all asking to download the files at the same time, and if you wish to get a good download here are some strategies:

• Go to a network with an OS X Server Caching service so that the first person to download the package will cause it to be cached so that all the subsequent downloads are a local transaction
• Use iTunes (or Safari) to download the update rather than perform an over the air (OTA) update as shown above.
• Wait out the rush and get your update several hours or days later.

Hopefully, enough servers are available so that this isn't "normal", but even on a fast connection to the internet you might have some delays in upgrading on launch day.