When I get on the ship, I turn off my phone and don't use the computers. Your either paying for internet service on your laptop. They have packages 100 minutes for $55. You purchase this on the ship. Or you are paying your cell phone provider. Both can add up quickly. I've heard from others that Skype doesn't work on the laptops because the speed is very slow. For example, printing off a boarding pass can take as much as 25 minutes when connecting via laptop.
If you are visiting one of the us territory islands, you will not pay any extra charges. I have sprint and I'm not charged roaming on St. thomas and Puerto rico. These are the only islands I turn my phone on.