Currently, I am sharing a Verizon Family Plan with 2 other family members. We all have regular, Samsung phones. Nothing fancy. The plan includes unlimited texting and 700 minutes of talk. I want an iPhone 4 but I do not want to increase the rates of the plan. Is there any way I can buy an iPhone 4, add it to the plan without making any changes (not adding a data plan) and keeping the same exact rates we have right now?

No it's not possible. I've tried many times. Verizon will not let you because the iPhone is a 3G smartphone so you need to get the data

No, I do not believe there is any way to add any smart phone to your plan without adding a data plan. I believe that if you buy a Verizon branded iPhone 4 to your plan, you will be charged an additional $30/month for the data plan if it can be grandfathered in. I do not think they like to do this, since they want everyone on their new "Share everything" plan. If so, you will really be out an arm and a leg from what you pay now.