The same thing happened to me this weekend, something very similar to one of the users here, I used my phone all night and it died (something that rarely happens to me) but I used up all the battery juice, when I got home I plugged the phone onto my computer and the first signs it was getting messy was that the apps would crash, the text would look fuzzy at times. Come Sunday morning I was texting my friend and the phone finally gave up, I got the infamous red screen of death, after many attempts to put the phone in DFU mode it finally stopped working, took it to the Apple store and the genius that helped me said that this was the 3rd time that day that she had seen this!! She didn't know what cause this and now she just hoped her own iPhone wouldn't have the same issue in the future, even in front of her I got a blue screen so I got a replacement in less than 25 minutes.
So my advice to everyone, don't waste your time with all these people saying it's a simple fix and that it just needs the newest firmware!! Plain and simple THIS ISSUE HAS NO FIX! Take your iPhone to your local Apple store or call Apple customer care so they can ship you a new one.