i've really had great luck with a straight razor and getting it off this way. as if it were a vinyl sticker on your car window... so hold the razor at a sharp angle so you don't scratch the plastic... a sharp one, with no dents or damage to the blade,
however.... lately i've been playing around with using fine grit sandpaper here, after most the old adhesive has been taken off. it covers up any minor scratches you may have made, gets rid of the last of the dry adhesive, and also makes a better clinging surface for the new screen protector.
if you try this, wash your case afterwards, it will remove the very fine plastic powder (which can cause the new adhesive to not stick as well).