Here’s what worked for me. Use a paper towel or rag, get it thoroughly wet with water, and press it onto the back of the sticker. Hold here for around 5 minutes. The sticker then should be able to peel off, even in the circular pieces that it is cut into. If it still isn’t coming off easy, simply hold the wet paper towel on there longer. See credit here.
I imagine this problem will be obsolete eventually, as the new stickers I have seem to be easy to remove. But somehow, our recently purchased car had one of the older registration stickers on it that are designed to self destruct upon removal. I assume this was meant to be some sort of security feature to prevent the stickers from being stolen. However, in my opinion this is a classic example of overdesign – the pain of removing these when you actually need to remove them verses the cost of having one stolen (they’re only worth like $50), is way out of balance in my opinion.