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I had iPad 1 with me since launch and cleaned with eye glasses cloth frequently without a problem.

Now I have the new iPad and just a week ago I actually put a scratch on the screen by my beloved eye glasses cloth, I still can't believe it but I SAW the scratch happen when I slowly buff it.

So I ordered screen protector from SGP........
 
Zagg HD. Will not use the iPad without it on. Feels like glass, no orange peel and protects it from any scratch. Love it!
 
Never on any of my iPads or iPhones....hate them much like wearing condoms...hate that too.....
 
For a buck fifty and peace of mind I figure why not, so long as there's no perceptible degradation in quality.
 
I used my New iPad for about a week before I applied a Magicscreen screen protector, the Crystal Clear (Invisible) Edition. It works extremely well, leaving no visible fingerprints and in no way diminishes the quality of the beautiful retina display. The peace of mind it brings is invaluable, especially when there are no real disadvantages.

One tip I'd like to share for anyone having trouble applying a screen protector is that applying it outside makes it a lot easier, as a breeze carries away any dust and leaves you with a nice clean work space. This is dependent on where you live, obviously if you live in a hot climate with lots of bugs and not much wind it's rubbish advice, but I live in Scotland where it's too cold and windy for anything to live, so it's fine for me. :D
 
sgp steinheil ultra optics

just got one of these, thankfully got it installed without any noticeable bubbles. it's expensive but I really wanted the anti-glare for reading outdoors. even under shade I find my new iPad has too much glare.
the screen is definitely not as sharp as it was naked, but definitely still sharper than my iPad 1 screen without a screen protector. my only other complaint is that the smooth feeling of the glass screen is gone, now it feels like I'm rubbing my finger against paper.
 
Like others have caught on, not all screen protectors look/feel the same. I'm using the one that came with my Switcheasy Canvas case. Hardly know it's there as it's clear, thin, and rigid. Been on for almost the last year.
 
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I'm definitely using a screen protector. I don't want to take any chances. I have in the past scratched glass surfaces on other touch devices.
 
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