I've been having this problem as well. More so today when I tried updating two apps and a message came up saying Cannot connect to iTunes. I tried searching for some answers on the web but only found things from 2008-2011. I synched with iTunes, restarted my phone, hard restart, and finally tried downloading something off the cloud to see if it went through. Once I did that everything went back to normal. Really annoying problem. I'm on a Iphone 4S for Att btw.
I had this problem a few days ago. The only way I could install was through iTunes. I finally fixed it by going to Settings > General > Reset > Reset All Settings. It reset everything, but didn't erase any data. After the reset you have to turn off then on iMessage and Facetime to get them to work properly again.