I recently discovered a quite remarkable product: an apparently very hard, fairly rigid, and extremely transparent plastic screen protector that clings to a camera LCD (or tablet computer, smartphone, etc.) without any glue or snap connectors. A thin, silicone gel coating holds it in place—you apply the plastic overlay from one end of the screen to the other, squeezing out the bubbles as you go—and it pulls off without leaving any residue. The product really stays put once properly applied; I can't imagine it accidentally coming loose. The manufacturer claims each shield can be removed and reused many times. The material seems quite scratch-resistant. I doubt it provides as much protection as the tempered-glass screen covers I have used on my DSLRs before, but I kept losing them and decided to give this product a shot. Also got a non-glare version for my iPad, which makes reading somewhat more pleasant outdoors.
The product is called "Expert Shield," and it's available from the company's eponymous website or from Amazon (at least, Amazon-US).
(I have no connection to the company or anyone associated with it.)