When I update to the latest iOS 8 today, my iPhone was stuck around 80% progress, and iTunes has an error 3014.

Error 3xxx has got to do with communicating to Apple servers, and something failed along the way. It could be your firewall, host records, internet connection, cable, etc..

This is what works for me:

Firstly, when stuck, you have to unstuck.

Press both the Power + Home buttons and hold for 5 seconds. It will force restart.

The device will then be connected to iTunes. Select restore to start over again.

Yup, just start over again.

I repeated 3 times, each time stucking at different progress. 80%, 25% before suceeding at 100%.

This is got to do with network connection, and the chance of getting stuck is random, especially so when 1 billion people is trying to update the latest iOS.

If each time you repeat and the progress are not stuck at different progress, you might have some other problems with your connection. Refer to Apple support page on some other solutions.

For me, restoring repeatedly works. Dumb, but it works.