I was having the same problem that many of the people posting in this thread appear to have been having. I had backed-up my iPhone 5 in iTunes, connected my new iPhone 6, selected to "Restore from prior backup", used my 5 backup, and, during the copying over of the applications to my 6, the process would seem to hang. I tried leaving it for several hours, but, no, it was indeed hung. Disconnecting and reconnecting the cable would start the process over again, but was a REALLY SUCKY solution.
I did not have any luck with (or without) the WiFi sync - it made no difference. Similarly, using the cable that came with the 6 versus using other cables versus going through a USB hub versus plugging in directly to the computer - none of those made any difference either.
In my desperation, I used CleanMyMac2 to uninstall iTunes and install a whole new copy from the .dmg downloaded from Apple. Still no difference. I also tried various restarts (of the computer and the phone), restores to factory settings (of the phone), etc. None of that worked either.
So here is what finally worked for me - simplifying the restore by unselecting items in my old 5 before backing it up again.
Just so we're all on the same page. I'm assuming that you own some older iPhone that you were using, and now you have bought a new iPhone 6. If you did what Apple instructed you to do, you backed up your old phone, went and bought the new 6, connected it to the computer, and are now trying to restore the old phone's backup onto the new 6. The 6 may be active with your cell phone carrier, and your old phone may be deactivated from your cell phone carrier, but I don't think that matters at all for the steps below.
Step 1 - update your old phone to iOS8. Others in the thread have mentioned this, and I agree. The fact that your phone is no longer active with your cellular service does not matter.
Step 2 - OPTIONAL - This step just simplifies things further, but I am not certain it is necessary. Go back to your old phone and log out of iCloud and iTunes. Logging out of iCloud may delete some data on your phone, so if you don't want to do this step, I'm not certain it is necessary. I list it simply because it's what I did.
Step 2 - Sync your old phone again with the computer.
Step 3 - As part of that synchronization, deselect the syncing of photos (that was the key for me), movies, music, podcasts, basically anything that you can re-enable syncing on later and not lose anything.
Step 4 - Disconnect your old phone and turn it completely off.
Step 5 - Connect your new 6. If it is not already reset to factory settings, and if it is practical for you to do so, I would suggest doing that. I did it by using the "Restore iPhone…" option through iTunes.
Step 6 - When presented with the option, in iTunes, to set up your new 6 as a new device or to restore from a prior backup, choose restore from a prior backup and select the backup you just made of your old phone. With photos, music, movies, podcasts, etc. syncing turned off on your old phone, when restoring from that backup, those will also be off on your new 6. Which means, the only thing that should be copying over are the applications. For me, this proceeded smoothly at this point and did not hang. If you are still experiencing hangs, try going back to step three and deselect more items. If that still doesn't work, then you are experiencing a different problem than I was experiencing.
Step 7 - Once everything completes, you can go back in and reenable the syncing of of all the things you deselected at step three. I would suggest selecting only one, then syncing your new 6 and letting all of that copy over, then selecting another one, then syncing, etc.
Step 8 - If you did step 2, then make sure to log back into iCloud and iTunes on your new 6.
Once you are done with all of those steps, your new 6 should be set up.
DETAILED EXPLANATION
From what I can tell, my problem at least appeared to be that iTunes was trying to do too many things at once. In particular, for me, it was the photos that were messing everything up.
Which brings me to my next point - has anybody checked the size of their Caches folder? The one in the Library folder in your Home directory? My Caches folder had ballooned from approximately 1 GB to over 9 GB! Using Finder to look at the files and folders in the Caches folder, I couldn't find anything that was taking up that much space. However, using Terminal, I found a folder (apparently invisible) called something like "Clear on Restart" (or something like that*). And it was CHOCK FULL of iTunesPhotoSync .mthmb files. Like thousands of them - all with different numbers after the "iTunesPhotoSync" part of their name. About 8 GBs worth.
*the folder is now gone and I can't find the exact name anywhere - if someone does find it and could post the exact name, that might help people who use the exact name as a keyword search to find this thread.
Anyway, I deleted my entire Caches folder after I did the above steps and got my 6 set up properly. While I don't necessarily recommend that you delete your entire Caches folder, those with experience in Terminal might consider a targeted rm -R directed to that folder that I described above (but whose name I can't exactly remember, sorry).
Hope that helps someone.
