I've just cured mine by doing a hard reset.
Turn the phone off. Leave it for a minute or 2.
Then turn back on. As soon as you see the "apple" icon, press and hold the "home" button until the apple disappears, then try the App Update. Mine worked.
Hope this helps.
OK, I had this same problem with the App Store on my iPhone 5 running ios 6.1.3, and also on my iTunes on all my computers. My Wife had the same problemn at the same time and here's what we did fixed both of our phones.
I had a feeling that it wasn't the phone or the App Store cause the problem wasn't wide spread enough. I thought it might have something to do with how the devises were comunicating with Apple, probuably something I did wrong and was unaware of.
First we tackled our Mac Mini's, and downloaded the latest iTunes from apple. We did have the latest iTunes installed on our Mac Mini's, but we downloaded it from Apple, and installed it again. Then we opened Disk Utility and ran the 'Repair Disk Permissions.'
Then we restarted our Mac Mini's. When we went back to iTunes, the apps downloaded without any problem, no delay, no stopping.
With the App Store and Itunes working well, we then synced our iPhones with our computer. After the sync was finished, everything on the iPhone worked like new. We did not have to Restore our iPhones or reset them. Apps downloaded on WiFi and G3 just as they did before.
It worked for us, and I hope it workes for you too.
Message was edited by: PaDale