No, doesn't bother me really. I got one of the Belkin rubberized 'backs' for mine so that the soft plastic iPhone case wouldn't become scratched and have an impact on it's resale value. The glass is actually quite durable, and I always keep it in either my 'man bag' or a jeans pocket where I don't keep change or keys.
A friend of mine had one of those plastic cases on his that covered the face. He has to press harder, but he dropped it face down once on a concrete floor. It cracked his case, but no phone damage.
I don't worry. Had the phone since opening day 1+years. Almost impossible to find any scratches on it, definitely none that can be seen while I am using it. To quote a wise friend "It is difficult to control and enjoy something at the same time"
A film protector won't do much at all to soften impact, but a good one should protect just fine against incidental scratches to the glass. I use the Power Support anti-glare, and although it's a bit of a sacrifice in terms of the beautiful clarity of the display, that's balanced out by it being nice and resistant to fingerprints and other smeary stuff. And nope, I don't work for Power Support!