I had this problem happen to me. It wasn't immediately after upgrading to iOS 8, but it never happened before either. There were no recent apps installed. The only thing I did differently was to leave the phone on the charger overnight versus the 1 hour or so I typically charge it. I usually let the battery drain to near 0 on a regular basis. It blue screened in the middle of the night while on the charger.
I attempted to do a factory reset/restore via Itunes. I kept getting error code 40 or other similar errors partway through the restore. I left the phone sit a few hours, then the restore worked. However it blue screened again very shortly thereafter. After doing this a few times, I got the phone to go on an endless blue screen reboot/cycle. I decided to let it sit and completely drain the batteries (which it did overnight).
The next morning I was able to plug it into my PC, do the complete factory reset/restore without an issue. Several hours later it is still working - but lets just say I am not very confident. The one constant was that the battery was being charged, or plugged into iTunes with this happened with a battery that was at or near 100%. Doing this from a completely drained battery worked and no issues so far.
All of the solutions - change USB cable, port - even different PC didn't work for me. The only thing that did work was to allow the battery to drain 100% and then do a the factory restore/reset. I will keep an eye out if this happens again and if it is when the battery is fully charged. But I was almost ready to bring this into service - drain your batteries and try to restore multiple times...I was suprised the first time it restored was after about 5-10 repeated tries.