Are you going to a region that uses gsm? e.g.. Europe. Verizon uses cdma in the US but the iPhone and many android phones also have a slot for a sim card. Verizon will usually unlock the sim part and you can buy a prepaid sim in your destination country.
I have a German sim that has good rates. I can buy 5 gigs of data for 15 euro!
I am now on Tmobile which has great international rates. My iPhone has automatic wi fi calling so I call call any phone in the US for free. Non wi fi calls are only .20 per minute.
up to 3G data is unlimited as are texts.