Nope.. no protector needed
As long as you don't scratch it with diamonds (rings/earrings), mineral crystals etc, it shouldn't scratch under normal circumstances.
I used to use screen protectors (PowerSupport is my favourite) for iPhone 3G, 3GS, 4. Both Anti-glare and crystal. Issue I have is that those screen protectors attract finger prints and it gets very nasty after about 1 year time.
With my iPad, I had the PowerSupport screen protector on as well, however I can no longer stand the anti-glare as it makes the display "grainy", especially on a retina display of iPhone 4 (4S). Crystal screen protector is "almost" invisible but then you can still tell that the screen doesn't look or feel as nice with the screen protector on.
With iPad 2, I use no protection other than the apple's cover so I can lay it face down when it's not in use. The screen so far is still spotless. (of course... my fingers and nails are softer than the screen so it won't scratch

)
I know a few people using iPhone 4 "naked" and "without protection" for 15 months, and the worst case i've seen is a hairline scratch that can only be seen if tilted under the light at a certain angle.
So no... Not protecting my iPhone 4S this time around as far as screen film goes, I would get a bumper or a lightweight case just so it doesn't touch the table top directly when it lay it down.