I do have screen protectors on my iPad3 & the wifes iPad1. I should add that I used the iPad 1 for 18mths without a protector and the iPad3 for a few months, and the screens were still like new, that is...until my wife let the grandchildren use her iPad1 when they visited, and now it has 2 small scratches on the screen, not bad but they are visible especially on black screen. Their own iPads and Ipod touch's are also scratched so after that, for peace of mind I decided to fit screen protectors to both.
Having tried a couple so called antiglare protectors which were actually not cheap, and imo degraded the pic quality far too much to be acceptable, I now use the very thin Technet branded cheap crystal clear 6 in a pack one's. They are very difficult to put on without getting dust particles causing small bubbles which cannot be removed because its specs of dust thats causing it.
However, after much practice I have now got it down to a fine art, and can fit them without any dust at all and without even a single bubble, so it is possible to do, and once fitted one has to look really close to tell there is a screen protector fitted and any loss in pic quality is barely noticable, but AIS they can be a pig to fit.
Don't even bother trying in a normal room, as it will be almost impossible to fit without a few bubbles, the trick is to run a hot shower in your bathroom for a few mins, then let steam subside a little, NEVER turn the protector over, always keep the surface that goes onto your screen facing down, I would also suggest before you start that you place a length of tape attached to the edge of the backing, which will enable you to peel the backing away slowly when you fit it so that no part of your hand or arm is ever over the iPads screen. Normal air bubbles always come out easily, but just one spec of dust especially if not on the edge where it may not matter if covered by a case, means you have to start again, hence the reason they give you 6 in a pack...lol
I admit it can be a frustrating experience trying to fit them perfectly, but when fitted properly without any bubbles at all they do give you peace of mind especially when your grand children pop in..lol Anything fitted over the screen has got to reduce the quality to some minor degree thats commonsense, but the new easy fit type which guarantees no bubbles and only available in antiglare are IME terrible for pic degradation, they are much thicker and tend to have a black border on them which is there to hide the adhesive underneath, there is no adhesive or anything in the centre, it's just around the sides, so in theory you would think it should work better. Sadly thats not the case, they are way too thick and the antiglare effect really degrades the pic quality a lot.
I spent over £60 on those and ended up throwing them away.
My advice is to just be careful with your iPad and no protector is necessary at all, if there's a risk it may get marked then learn how to fit the very thin crystal clear ones as they do give the best result with minimum degradation and they are dirt cheap, expect to scrap a few at the first few attempts, but with patience and care it's possible to fit them perfectly everytime.