I can't live without my internet. I like the plans where you can buy a lot of minutes and of course free wifi is best. You won't want to use your cell phone in international waters, it gets very costly, so be sure your data and phone service is turned off if you use your apps. I turn my phone off and use my nexus so there's no chance that I'll get charged by the phone company. Many of the ports have internet cafes or places to get your email, but who wants to spend the time in port doing email? The answer is yes, and I even skyped home each night without any issue on my last cruise in the Mediterranean.
I purposely turn off my cell phone and avoid email to truly disconnect when on a ship. I have to keep a cell phone on all the time for work (medical field) and have to admit it is nice to not hear it ring or answer emails. I think people need time away from electronics to relax. My husband and I sit and talk even more and enjoy our time together. Our family knows how to reach the ship in the event of a true emergency. They all know once I board a ship, I am truly on vacation. LOL