I put a case on them, but rarely a screen protector. I keep mine in a holster so the chances of scratching the screen are low. Also, I have a "pouch" type mount for the front of my bicycle that keeps it behind fairly thick plastic, and the screen responsiveness is already reduced using that - anything more separating my finger from the screen would probably make the phone completely non-responsive when it's in the bike mount.
I ride in the rain and snow a good bit, though, so I need the protection of the enclosed phone mount when riding.