I haven't used screen protector for years. Never had one on my iPhone 4 or my 4s or my Galaxy Nexus or my Galaxy Note 2. Never had a problem. However
on day 16 with my gorgeous new s4 I noticed I have a tiny little pock mark and ever so tiny short little scratch right dead center in the middle of the S-View window. Make no mistake its on the phone screen itself and you can actually feel your fingernail dip in when you rub across it ever so slowly.
You can only really see it when you turn the light just right but it still makes me incredibly nauseous just the same.
I would absolutely recommend one and Ghost Armor was always my favorite before. Worst case scenario is you use the screen protector for 3 months and decide that you really don't need it and when you peel it off the screen is just as mint as the day you got it. That's a win win and damn good peace of mind IMO, I'm telling you from experience both