I've never used a screen protector on either my 3G or my 3GS. My wife doesn't use a screen protector and neither do any of my friends who have an iPhone.
The screen is glass, and it's only going to get scratched through carelessness, or being a dirty person with sand in their pockets (or a rich one with diamonds in the pockets 🙂).
As for the screen breaking, that's a very real risk, but protectors don't do much in this regard. Better just to be careful, or if accident prone then put it in an Otter Box or similar klutz-proof case.