Based on prior years, Game of Thrones will be in the VOD sometime after the first of the year prior to its March new episodes. What is available is totally up to the broadcaster not Verizon.
HBO determines which episodes are available On Demand. Like another poster said, the full seasons of the HBO shows can be found via HBO Go. If you want to watch HBO Go on your TV, I recommend picking up a streaming device like a Chromecast, Roku, Apple TV, etc.
It is accurate that comcast has all the HBO series available, which FIOS does not. I have gone through customer support and technical assistance with FIOS. They tell me it is a contract issue with HBO. I believe it is set up as a way for Verizon to make more money. I intend follow up with Verizon management (marketing specifically) about this, as I am already paying for HBO and Showtime allows me to look at all seasons of all shows.
You have access to everything via HBOGo.
Comcast quite possibly has a better deal than Verizon due to the fact they have a much larger customer base.
Verizon doesn't pay enough to HBO to get Game of Thrones on demand. It might be worth canceling your HBO subscription on Verizon and getting HBO Go when it becomes available this year (due in 2015). Its in the works to be able to subsribe to HBO indepedenty of your tv provider.
Of course, that's assumes we have net neutrality. Currnetly, a cable provider can choose to prevent or slow access to streaming services like Netflix or HBO Go.
But you already have access to HBOGo.
So why not keep paying Verizon so you can watch both regular HBO and use HBOGo as needed for the same price?