Yes, you do need a screen protector. I use my phone as badly as I can, but the only part which concerns me the most is the display, I take pretty good care of it, and when I take good care of something it's good. Yet I couldn't manage to not scratch a display. The only phone where I couldn't manage a scratch was Galaxy S2.
I will always recommend a good glass protector. It will not only protect the screen from scratches but from shatter too in case of an accident.