We recently upgraded our phones to the iPhone 6 and only 9 days into the month we are getting a notice that we have used 75% of our data. We aren't using the new phones any more than we were the old ones so how could we have gone up this much? I assumed the new phones might use a little more than the old ones but we never had a problem staying well within our data on the old phones so how could it be up so much? Are there some settings we should adjust on the phones?
How many new iPhones did you get? In the process of setting up and customizing your phones did you use Wi-Fi or cellular data to download and install apps and perform updates?
You didn't say what you upgraded from and how many iPhone 6's you have on your account. If you went from 3G phones to iPhone 6's, you're now using data at a rate up to 10x faster than before and while you perceive yourself to be using your phones the same way as always, you really aren't. Fifteen minutes of internet use under 4G would consume up to 10x more of your allotment than under 3G. Think of it as a faucet where 3G would be the equivalent of a trickle and 4G would be as if the spigot were wide open. Under 3G you might take 60 seconds to fill a 1 gallon container but under 4G that 1 gallon container would fill in about 6 seconds. Verizon offers many tools for managing your usage and they're definitely not gouging you. They provide the service and its up to each user to pay attention to how its being used.
To see what specifics are being used, I suggest installing a data usage tracker (there's a good one in the App Store by Onavo) and set it to match your bill cycle. Do that for each iPhone. Apps like that will give you a list of specific activity, such as web browsing, use of Facebook, video streaming, etc.
See how much date each app is using by going to Settings > Cellular and scrolling down. You'll see the individual apps and their usage for the current period.