My iPhone died the other day. When I took it out of my pocket I noticed that it was hot, but when I tried pressing the home button, nothing happened. I tried the power button, I tried holding down the power button, but still nothing. Then I tried plugging it in, in case the battery had run down. Still nothing. No sound, no screen, no indication besides its heat to let me know it was anything but plastic and glass.
Finally, I plugged it into my computer and started up iTunes, which recognized that the phone was there, but wasn't able to do anything with it. It hung backing it up, and it hung canceling the backup. There's an Apple store near where I work, and I considered taking it to them, but I didn't want to ask for help until I had at least rebooted the darn thing. The problem was that there was no way to reboot it. I suspected it had simply hung, and was now unresponsive. You could use the power button to turn it off, but first you had to hold it down, then it would prompt you to swipe the screen to shut it down, and as I mentioned, there was no response when I hit the power button. I couldn't even take the battery out, since the iPhone doesn't give you access to it.
Ultimately, I had to let the battery run down. When I charged it back up, it was fine. But this has convinced me that the iPhone really needs a hard reset.