The connection was always so painfully slow for me that I gave up after a few cruises and now cruise completely disconnected. And I can tell you that it's made a wonderful change in my vacations, the feeling of being away from all that for a week is pretty magnificent, and after the first time it doesn't bother me not knowing what's going on.
That said, on the Magic in January I was floored by how good the wifi connection was for a guy I met who bought some minutes. He bought 500 minutes, and used on his ipad. The internet was screamin', as fast as wifi in a coffee shop it seemed. He was doing video chat (facetime), streaming videos from YouTube, streaming music from Pandora, and uploading all his photos to facebook as he went. He even facetimed the fireworks show to his wife at home so she could see it live. Even on sea days his connection seemed rock solid.
The guy next to me sat on his balcony every night with his laptop checking in on the day's activities, and he said the connection was better than he's ever had before. He had no issues, even commented that it was like working on his wifi at home.
So, at least on that cruise, the connection seemed to be fine for the people I talked to.
I agree with some PPs, if your kids want it to post instagram pics as they go, let them know what it costs and let them pay for it if they think it's worth it. That's obviously a personal decision for you and your family, but for something that's so expensive and not really necessary I think it's a good opportunity to teach your kids the value of money.