I've dropped mine many many times onto wood and concrete without a screen protector. The phone is a little chipped and scratched, but the screen is absolutely fine.
A nilkin tempered glass screen protector is a good investment as it feels brilliant although when I dropped mine with that on it smashed the corner of the protector.
The edges of the phone are slightly raised so without the screen protector on, a drop onto a flat surface will not damage the screen but will damage the screen protector.
A drop onto a raised surface like a stone would probably break the screen protector but don't know if it'd also damage the screen.
Question is, how often do you drop your phone, and how much do you want to spend on glass protectors?