I hate screen protectors on the Z - the 640x480 screen suffers too much with the protector. (And I was using the official Japanese $10 protectors...)
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My experience is quite different.
There are several types of screen protectors: some make the screen fuzzy and scratch easily, some are difficult to remove as they leave a residue etc. -> these are about 95% of the screenprotectors sold ( based on ads etc.)
These are the ones I used in the past on my Palm, Psion etc. ( I have sold several PDA's in the past: all got a good price, since their screen was 100% scratch free)
However, I have bought recently a Sony PSP - and for the PSP a Hori protector.
The Hori protector was nothing like what I have had before. It is a totally different material, it requires a different approach to put it on, but when its on, it is virtually invisible. I have shown it to several people - about half have not realized that a protector was on at all, the other half agreed, that is is invisible ( you can see the edge, that is the only way to see).
As LCD screens do scratch (especially if it is a touch-screen), and the scratches are very difficult to remove (and during the removal process one can damage the screen) I tried to find a screen protector for the C3100 - similar to the PSP one.
And I have found it: Ultra Clear Screen Protector for Sharp Zaurus SL-C3100/C3000/C1000 - US$12 shipped from pdair.com
After application it is invisible, the screen quality is exactly the same what is was before - and it is protected from scratches. It is not easy to put on ( as the bottom surface attracts dust etc. ) but after about 45 minutes it was done.
It has been on now for a couple of months, and I have no scratches, I am not scared to wipe off the screen ( which could scratch it w/o a protector) and I have a screen which looks the same as w/o a protector... (Some people prefer to write on the screen protector vs. the unprotected screen. I feel no difference...)
Conclusion: always use a screen protector to protect your expensive electronics screens....