If I buy an iPad 3 on Verizon, can I use my existing SIM?
The answer is YES. I purchased a Verizon iPad 3 from someone on craigslist, I then tried cutting the sim card from my Android 4G LTE phone ... fail. I bought a new sim card and ordered a Noosy from Amazon, cut the new micro-sim and VOILA, it worked! Unlimited data on my iPad 3 :)

You can see how i did it here:
http://inboxi.us/ipad