I find the case has a bit of a ridge around it that protects the glass. Our first phones always had screen protectors on them, but they always produced bubbles, and made the keyboard harder to push. For the past 8 years or so we have not bothered and never had a problem with broken or cracked...
My wife took her leather iPod cover to a local shoe maker, and had wrist strap put on it. It is one of those large ones that are easy to drop. She has not dropped it since.
I have found that those plastic sheets do nothing but make the touch screen harder to push.
What has really worked for me is the rubberized case that my iPhone pops into. I don't want to jinks it now, but I have had my phone drop a number of times -- sometimes with a loud bang, and the glass...